Tight on the shaft, but loose inside the wheel! The bearings may be slightly undersize on the O.D. .... I donno?
That would certainly cause a wandering, wobbling issue.
Can you accurately measure the new VS the old bearing outside diameters?
How you can make them fit better is a machine shop question, but you can't really do anything with the bearings themselves, only deal with the wheel. A few ideas come to mind:
A version of removable Loctite may take up any difference.
Dimpling the area around the recess with a center punch may "upset" enough material to make them snug.
If you have to remove the wheels and have a machine shop sleeve them, that will be expen$$ive.
A cheaper approach would be a different brand of bearings, but use an OD the same as the old ones.
Good Luck to you on this issue!