"you can get like 600 free skill points out of it along with maxed unarmed skill"
If you want to keep your unarmed at 300%, there's no way that you'll be able to get 600 free skill points on top of it. That would be one hell of a free lunch
The free skill points from Tag! is more along the lines of leveling up some skill for free, (like Science, can be leveled up to 127% just by reading books), then tagging the skill and lowering it to the pre-Tag! level, pocketing the delta. So you get ~200 or whatever of skill points for the perk slot and the skill remains at 127%. But unarmed doesn't have a book. To get 300% after Tag!, you need to increase unarmed to about 175%-180%. But in your case you want to Tag! it beyond 300%. I couldn't be bothered to math it so I cheated myself 20 levels worth of xp. To get to 190% Unarmed, it took me ~400 skill points, then after Tag! and lowering Unarmed from above 300% to just 300% I pocketed about 100 skill points, so I'm still ~300 skill points behind. There's about 45 "inflation free" Unarmed training skill points (of course the price paid is ugly meta-gaming, similar to doing a Navarro run) so even with those I'm ~200 skill points behind.
Also to test it I had to downgrade sfall to an older version, 4.1.1 (2018). I kind of wonder whether the bug with Tag! doesn't exist solely because of sfall.
Thief has a similar bug (taking the perk, then lowering skill to pocket the difference; and I assume other skill gaining perks have the bug too) - I was a bit surprised when I found out that you can't lower your skill after Thief in non-sfall vanilla. [EDIT: nah, I guess it must have been in vanilla too]