After Effects slow animation
I was going to recommend nesting the comp and use time-remapping actually, which of course you came up with as the solution. 

I think, to be honest, this is your best bet, or time remap each layer in your existing composition. 

Doing the time-remap on your original comp, has the advantage that the keyframes will in fact be at the correct place given whatever time-base you want to end up in. This will allow for, if say your time-base is higher, more discrete frames, or points, in which to place new keyframes. 

Doing a remap in a nested comp will limit your ability to add keyframes in between what would be 2 frames... being your master comp (parent) only has 1 keyframe and therefor cannot be divided. 

Try time-remapping the composition; after you adjust the composition settings to the correct timebase. I don't see why that wouldn't give you what you need.