>> I don't see any way I can bury those stems to get new roots growing.
Here are some possible speculations that you may have already considered and discarded.
If you're willing to sacrifice one or two big nursery pots, you could make a collar. Cut out the bottom and slit it up the side. Pull it open and wrap it around the plant. Push it a little ways into the soil, between the soil and the white pot's sides. If the white pot is bigger than the nursery pot, use a second slit nursery pot to cover the gap. Duct tape them together, and maybe duct tape the collar to the white pot. Filling potting mix.
If you had some stiff plastic, you wouldn't have to sacrifice big pot.
Or ...
Have someone hold the plant and trellis, lifting it up while you remove the existing pot. Assuming the root ball doesn't disintegrate, plop the whole thing back down into a wider, much taller pot, like a 5-gallon bucket.
Or maybe just drop the existing pot into a 5-gallon bucket and fill the whole thing with soil, as deeply as you want new roots.
