My guess would be that you should treat the black areas on the base with peroxide as well. This should stop any rot that has spread to there.
I've never had to do this myself though so I'm just going on what I have read. I know people put peroxide in the crown to stop rot there... so why not use it to stop rot at the base as well.
Personally if you have any good root left I would pot it up with as small an amount of bark as you can get away with. If you can't get a small pot, or you think the pot will overbalance with the big plant, then use packing peanuts in the base (not the ones made of corn starch) to pad out the pot then just have the medium at the top.
This is what I have done with one of mine which lost most of it's roots. I took an upturned yogurt pot and cut large slits in the sides. I placed this in the bottom of the clear plastic plant pot. I then put packing peanuts to fill the gap arround the yogurt pot, then potted the Phal in a layer of bark at the top (just deep enough for the roots).
I tried with just the yogurt pot initially but the bark arround it still did not dry quickly enough. You need to ensure that there is not a mass of bark with no roots in it which then never dries out, or you are back to the original problem that caused the rot.