The bacteria we want to grow live on every surface in the tank - the glass, the substrate, the decor on the heater etc. They grow best where there is a good flow of water - inside the filter is the best place for this.
I suggest you move everything you can. Even if the decor is not part of your long term plans for the new tank, in the short term they will help as there will be some bacteria on the decor.
The U2 filter has 2 sponges, 2 poly-carbon pads and a box of ceramic media. I think the ceramic biorb rocks are too big to fit inside this box. But the sponge from the box in the biorb can be 'persuaded' to replace the poly-carbon pads with the aid of a pair of scissors.
If you could get any of the smaller stones inside the U2 that would be a great help. How hard are they, can they be broken into smaller pieces? If the answer is yes, I would smash up as many as would fit inside the box in the middle of the U2 then do as you suggest with the rest in a mesh bag. After a couple of months start removing the stones in the bag a few at a time, then replace the broken stones bit by bit with the proper U2 ceramic medium.
A master test kit is definitely a good idea. Feed the fish lightly for a few days before the swap, nothing on the day itself, and lightly for a few days afterwards. Test for both ammonia and nitrite until you have a week of them both zero. If you do find either or both drifting above zero, water changes are the best way to keep them down. If you have a low pH to match your soft water that will help keep the ammonia in the less toxic ammonium form, but nitrite will be more toxic.
I know it will be hard to resist but if you could manage to wait a couple of months before getting more fish you will do yourself and the current fish a big favour.
What kind of catfish is whiskers? if you don't know, a photo could help with an ID.