Nice work on the roots. I would probably have chopped the remaining roots much shorter to encourage more root ramification closer to the trunk but that can be done another time if you mant to do it.
No problem chopping a Chinese elm at repotting time.
Chinese elm can be chopped as low as you like. Elms have the ability to throw new buds from the trunk and from the exposed cambium at the chop site so there's no real need to restrict chops to a side shoot or branch.
If the trunk is still unstable you can tie it to the outside of the pot. I sometimes use twine or wire wrapped around and under the pot then around the trunk. If the lean is only in one direction a simple wire hook from the trunk to the rim of the pot may be enough. Your tie down only needs to be in place long enough for the new roots to grow into the soil - maybe 3-6 months, depending on conditions, etc.
