I don't think there's anything to be gained by bringing up the voltage slowly.
Before powering it up though, jot down the values of the caps that look suspect. If they blow, you may not be able to read them later.
I also don't buy into replacing good caps to increase reliability. Bulging or leaking caps should be replaced, leave others alone. Removing caps from a printed wiring board is no easy task and excessive soldering heat will lift traces. Now you got a mess on your hands.
If you're looking for reliability then get a backup supply.
