I have a florian and Konsta modded v5 SS 4x4. Two of them actually, and they are both way better than anything unmodded. One cuts at about 40 degrees.
Two things. First, you can definitely over mod. It's a very real possibility. Considering how much better a fully modded cube is over a non-modded one, it's worth the risk. It sounds like your v4 may be over modded. I doubt the very tiny differences between the two versions could account for such a large perceived difference on their own. I personally believe that the florian mod requires just the right amount of plastic removal, not too much and not too little, to achieve the best results.
Second, while you don't have to touch the tensions when florian modding, you will absolutely have to re-tension the cube afterwards. The cube will feel much looser, it's pretty much a different cube after the mod. I find that SS 4x4s are the biggest pain to tension. Even minute adjustments are noticeable. It's worth the time it takes to get that perfect tension.
If you're worried about ruining your perfect tensions, then buy a new cube and mod that one. I personally would never go back to an unmodded SS after seeing how good they can be when modded well though.