I might have my facts skewed but I believe the problem is this: If the potion fortifies enchant for say, 30 seconds... that's 30 seconds in game time. What this means is that you'll never get the full fortify effect unless you hurry and you'll rarely get it when enchanting multiple items unless you are super fast.
You are correct. You can take your time renaming the item, but you need to pick what your enchanting, pick the soul and pick the enchantments quickly. Do don't have time to play around.
IDK if Fortify Enchanting is bugged or what because I used a +10% one once (Enchanting 100 with all the 'useful' Perks) and there was no difference between those and the enchanted items of the same type that I had created without a potion, but with Smithing I definitely notice a difference even with a 2% change.

Edit: I've read that by leapfrogging Enchanting and Alchemy Fortifies you can get up to +28% or +29% on gear. I've never bothered with that because +25% is good enough for me.

Your not going to make a potion of enchanting that causes a measurable increase without fortify alchemy items on. And by leap frogging you can get a lot more then +28% I have a guy with a few +250% of fortify enchanting hanging around.