Actually, as hilarious as this is, it turns out it's really easy to do this in WadAuthor, because WadAuthor lets you copy-paste the entire map into another window. Step-by-step:
1. Move all the tags to the new numbers. What I generally do is select all, and set the tag on every linedef and sector to ++100, then find/replace tag 100 with tag 0.
2. Copy-paste the map in WadAuthor because it's trivially easy to do this in WA.
3. Crack back open whatever editor you want to actually use to move everything to the positions you want.