This is a tricky question to answer because there's not really any way to make a step-by-step guide for it. This is inherently complicated, and revolves mostly around dozens of small changes to the game over time, with no one-size-fits-all solution. But as someone who has ported levels from old versions, I'll give you some things to look out for when porting the maps:
1. Flags. In the Final Demo era, object flags were mostly used to determine which difficulties each object would show up in, just like in Doom. This was one of the main motivations behind removing difficulties altogether in 2.0, to free up object flags to be used for other things. As a result, every object's flags will need to be reconfigured. For example, one of the object flags became "reverse gravity" which causes the object to spawn upside-down and on the ceiling. Since this flag used to be use for difficulty allocation, when you load into a Final Demo map, pretty much all of the objects are going to spawn on the ceiling.
2. The palette. Final Demo used Doom's color palette, while 2.0 introduced an entirely new palette, and 2.2 replaced that with a new one of its own. You'll have to manually convert every texture and sprite to the new palette. This can be done with the "Convert To" button in SLADE.
3. Software. Zone Builder did not exist until the 2.1 era, the most common map editor back then was WADAuthor. This is a considerably more archaic editor - in fact, it was so much harder to make levels that most maps were sketched out on graph paper first. I've never had to use WADAuthor when porting maps, I have simply loaded the old files in modern Zone Builder and fixed everything from there, but for a larger project like this, you might have to. Do not use UZB, it's designed for UDMF, while those old maps are binary.
4. Effects. Most linedef and sector effects have changed since the Final Demo era, and so most of the FOFs, PolyObjects, and teleporters will need to be manually recreated in Zone Builder. Fortunately, the SRB2 Wiki has kept articles on just about every linedef and sector effect since the Final Demo era, so you can go to the old versions of those pages to learn more about what's changed and how it used to work.
5. Objects. Multiple objects from Final Demo no longer exist in contemporary SRB2, or have been changed so much as to be unrecognizable. You'll have to manually recreate these old objects using SOC, which has also changed a bit since Final Demo.
This is just the tip of the iceberg, but I wish you the best of luck in your efforts!
