Belts can be had from Sew-Classic and many other places. Many times your LSMG will have them too.
It could be your belt is stretched. Try cutting off a 1/4" or so and see if that helps. Also oiling the treadle mechanism and machine helps reduce friction and that helps prevent belt slippage.
If the bottom of the cabinet droops when you pick it up, you'll need to remove the head and turn it upside down and re-glue it. Been there and done that with my Franklin parlor cabinet.
My method of reattaching veneer is to use a plastic credit card or a hacksaw blade to work glue between the veneer and base wood. Then I clamp or weight it so it stays till the glue is dried. I use Elmer's Wood Glue Max.
If your cabinet has sat in water you might need to re-glue the base wood too. The old glues don't hold up well when they got wet.
Joe