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A Hammer Jump addon split into 3 different styles, with each style being based on a specific version of the Hammer Jump.
"HJStyle_SRB2"
Advance Styled - Hold Jump after landing with her Piko Piko Hammer to perform the Hammer Jump, launching you higher than a normal jump. Like Sonic Advance, you can perform it from a standstill or while moving, but are left vulnerable and unactionable after using it.
"HJStyle_SA1"
Sonic Adventure Style - Hold Spin after landing with her Piko Piko Hammer with a running start to Hammer Jump. Like Sonic Adventure, her Twinspin can be performed after the Hammer Jump, as well as Shield Abilities.
SA1+ increases the height of the Hammer Jump based on your current speed.
“HJStyle_P06”
Based on her move-set in Sonic P-06 (A.K.A Sonic Project 06), a from the ground up fangame remake of Sonic the Hedgehog (2006)
Hold Spin after landing with her Piko Piko Hammer with enough speed to perform a Hammer Jump and leap forward with a boost of speed. It doesn't go as high, but Amy can also Double Jump after a Jump or Hammer Jump. Like Adventure, she is actionable after a Hammer Jump.
NOTE: To use Shield Abilities, hold Jump before pressing Spin.
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Also check out clairebun's addon to make her hammer abilities always be on spin.
NOTE: P06 Style does not have compatibility with said addon. Double Jump makes it complicated.
"HJStyle_SRB2"
Advance Styled - Hold Jump after landing with her Piko Piko Hammer to perform the Hammer Jump, launching you higher than a normal jump. Like Sonic Advance, you can perform it from a standstill or while moving, but are left vulnerable and unactionable after using it.
"HJStyle_SA1"
Sonic Adventure Style - Hold Spin after landing with her Piko Piko Hammer with a running start to Hammer Jump. Like Sonic Adventure, her Twinspin can be performed after the Hammer Jump, as well as Shield Abilities.
SA1+ increases the height of the Hammer Jump based on your current speed.
“HJStyle_P06”
Based on her move-set in Sonic P-06 (A.K.A Sonic Project 06), a from the ground up fangame remake of Sonic the Hedgehog (2006)
Hold Spin after landing with her Piko Piko Hammer with enough speed to perform a Hammer Jump and leap forward with a boost of speed. It doesn't go as high, but Amy can also Double Jump after a Jump or Hammer Jump. Like Adventure, she is actionable after a Hammer Jump.
NOTE: To use Shield Abilities, hold Jump before pressing Spin.
-----
Also check out clairebun's addon to make her hammer abilities always be on spin.
NOTE: P06 Style does not have compatibility with said addon. Double Jump makes it complicated.
STYLES [OUTDATED [v1a]
"HammerJump_Advance"
Advance Style - Press Custom 1 to Hammer Jump. This allows for an instantaneous high jump being performable at any speed, akin to its use in Advance.
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Changelog 1.1
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Increased Hammer Jump's power. (14 -> 16)
Added the ability to hit enemies while spinning.
Removed pointless P_SKIN file.
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Changelog 1.2
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- Fixed bug where dying during a Hammer Jump would not display the DEATH animation.
- Fixed bug where Hammer Jump animation would not work while in reverse gravity.
- Amy can no longer Hammer Jump while in "Thokked" state
- Updated SOC file.
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Changelog 1.3
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- Removed the ability to perform a "late" Hammer Jump.
- Super Form support: Her hammer strikes will cause powerful earthquakes, and her Hammer Jump goes up even higher.
- Can no longer perform Hammer Jump if she has the flag debuff.
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Changelog 1.4
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- Added a new "Piko Ring" effect when Amy's Piko Piko Hammer strikes the ground.
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Changelog 1.5
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- The Adventure Style Hammer Jump has now been reimplemented.
- To perform this Hammer Jump, use the Hammer Attack while running to go flying into the air. After uncurling midair, she can use her Twinspin Attack or Shield Ability.
- This Hammer Jump also launches slightly higher than the Advance Hammer Jump, as a tradeoff for only being usable at higher speeds.
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Changelog 1.6
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Hammer Jump Adventure
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- The faster your speed is when performing the Hammer Jump, the higher you go. Double your speed with the speed shoes or momentum! (momentum not included)
- Hammer Jump speed requirement has been reduced to 28, to be in-line with all the other character's runspeeds and to make it slightly easier to use on slopes.
- Hammer Jump's startup has been reduced to make it more like Adventure's.
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Hammer Jump (SRB2 and SA1)
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- Piko Ring Animation starts at a FRACUNIT instead of 0. This was a recommendation to fix a bug with FOFs (Floor over Floors), while it did not fix the FOF bug, I did think it was a good idea to include anyway.
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NOTE: I have removed the other style (Advance Style) due to redundancy, and it not being as well polished as it could. It is still available in the history tab however, along with the outdated versions of the Adventure and SRB2 Styles. ("v1a")
"HammerJump_Advance"
Advance Style - Press Custom 1 to Hammer Jump. This allows for an instantaneous high jump being performable at any speed, akin to its use in Advance.
-----
Changelog 1.1
-----
Increased Hammer Jump's power. (14 -> 16)
Added the ability to hit enemies while spinning.
Removed pointless P_SKIN file.
-----
Changelog 1.2
-----
- Fixed bug where dying during a Hammer Jump would not display the DEATH animation.
- Fixed bug where Hammer Jump animation would not work while in reverse gravity.
- Amy can no longer Hammer Jump while in "Thokked" state
- Updated SOC file.
-----
Changelog 1.3
-----
- Removed the ability to perform a "late" Hammer Jump.
- Super Form support: Her hammer strikes will cause powerful earthquakes, and her Hammer Jump goes up even higher.
- Can no longer perform Hammer Jump if she has the flag debuff.
-----
Changelog 1.4
-----
- Added a new "Piko Ring" effect when Amy's Piko Piko Hammer strikes the ground.
-----
Changelog 1.5
-----
- The Adventure Style Hammer Jump has now been reimplemented.
- To perform this Hammer Jump, use the Hammer Attack while running to go flying into the air. After uncurling midair, she can use her Twinspin Attack or Shield Ability.
- This Hammer Jump also launches slightly higher than the Advance Hammer Jump, as a tradeoff for only being usable at higher speeds.
-----
Changelog 1.6
-----
Hammer Jump Adventure
-----
- The faster your speed is when performing the Hammer Jump, the higher you go. Double your speed with the speed shoes or momentum! (momentum not included)
- Hammer Jump speed requirement has been reduced to 28, to be in-line with all the other character's runspeeds and to make it slightly easier to use on slopes.
- Hammer Jump's startup has been reduced to make it more like Adventure's.
-----
Hammer Jump (SRB2 and SA1)
-----
- Piko Ring Animation starts at a FRACUNIT instead of 0. This was a recommendation to fix a bug with FOFs (Floor over Floors), while it did not fix the FOF bug, I did think it was a good idea to include anyway.
-----
NOTE: I have removed the other style (Advance Style) due to redundancy, and it not being as well polished as it could. It is still available in the history tab however, along with the outdated versions of the Adventure and SRB2 Styles. ("v1a")

You can actually see the hammer frame before she goes into her "spinning state" while rising. Granted it only appears for a very small amount of frames. I feel like the ideal way to go about this would be to make sprites for her performing the hammer jump. You can kind of see her in her hammer frame while she's rising off of the ground and I didn't really want too much of that to be seen.
At least thats what I think. But yeah I do agree overall that most of the time using this move is better than using your standard jump, I feel like it has a lot to do with SRB2 being a 3D game and it's level design too though. There could also be other things about Sonic Advance's physics that I don't take into account of.
I could have made code to reduce the player's current momentum or speed when doing the move, but it just doesn't seem that hard to pull off a Perfect Hammer jump in advance and wouldnt want to make a move that would be inaccurate to the source material
I WILL SAY however, in some of the rom hacks of Sonic 1 and Sonic 2 that they put Amy in, Amy doesn't slow down in her crouch, she stops ***instantly***, therefore a perfect hammer jump is impossible in that case.