I could zoom so the sides hit the edge of frame, but then I loose a lot of head room.
==============
That’s what you want to do first. Then, slide the whole image DOWN so that the top of the 4×3 frame is now at the top of the 16×9 frame.
Now, third, you have to go though the whole movie and check every shot. There will be shots that you have to cut and slide back UP inside the frame. There will certainly be shots that should be vertically centered or perhaps bottom-aligned. Each shot will have to be checked…nearly every one will look best at a different height from the others. Even ones that look good top-aligned may look better if they’re 10-pixels higher. Or 5. Or 20. It’ll be up to you to pick what you like.
Time consuming, yes, but it will give you the best result.