Wow! You’ve earned my respect for not tossing in the towel.
I’m not familiar with the VK63 case and, without pictures, I can only guess. It’s possible that you may not need to shorten the pushers if it was only to insert the movement. Removing the pushers, will give you more room and you can reinstall them after the movement is in place. If they are actually too long, then a little haircut is obviously needed.
One thing not mentioned. Is your stem height. How does it line up with the case? Before buying a new case, double check stem height alignment. Too far off and you’ll need to pick a different case or this project is not going to end well.
That ring sounds like it might be a movement holder. If you could straighten the thing out, you may be able to repurpose it (with modifications?) to hold your movement in the new case. Again, without photos, I’m just tossing out my best guess.
Otherwise, if you measure the gap between the new case and the movement, you can purchase a plastic movement holder (or two in case things go sideways with the first) on AliEx. The nice think about the plastic holders is they are easy to modify and dirt cheap.
Cutting the stem should not be done until you have the movement properly seated in the case. Let’s get you to that point first…then you can post pictures and we can talk about sizing the stem. In the meantime, when you are ordering parts, it may be a good idea to pick up an extra stem or two.