Tony - Memphis
An other good source is Joewoodworker.com. I just bought some beautiful walnut burl veneer there that I'm using for a box I'm working on. There is some good info on veneering there as well. He sells a glue that works very well and is water based. I have had good luck with it.
I guess I would go at the old veneer with whatever worked to pry as much as possible off. I might trace the seams with a knife to avoid lifting anything other than the panel. After that, I might try heat - I use a household iron. Start low in a spot and see if the glue reacts.
I would try the glue at Joe's or even liquid hide glue. You will need a way to clamp the veneer as well. I use melamine as a platen and pond liner as a flexible layer (for even distribution) and wax paper to prevent sticking. Cauls might help to distribute clamping pressure.
Something to consider when cutting is the angle of your cutting edge. Your veneer saw is probably flat on one side - use that against your straight edge. In short, most cutting edges are V shaped in cross section and could result in a gap. I almost always cut from behind.
Blue tape is good to hold the veneer in place while clamping.
Check the thickness of your current veneer vs the replacement piece. Could be an issue. Hopefully, the new stuff will be a hair thicker.
Make sure you get as much of the old glue off as possible and check to see if whatever glue you use will stick!
Careful if using a scraper to clean up - those eyes will tear out....yes I have.
That's all I got. Good luck with it. Hope it works out well. For inspiration ,there are some really good videos by a repair guy on Youtube - Thomas Johnson Antique Furniture repair. He covers a lot of veneer repairs.
I learned a valuable lesson yesterday...rookie mistake. I was sanding the cut faces of a box I had cut apart and veneered the joint faces (where top and bottom meet). I was using a nice and flat sanding block. I guess the sandpaper was not good and tight and I ended up sanding the corners down a bit low. Just enough to result in a nice ugly gap! Darnit. This is highly figured walnut burl, so I am attempting to glue a small piece over the low area, then clean off the excess. The joint line may not show up and will hopefully look like a figure line? We'll see. This wood is gorgeous. I guess if this doesn't work I will either insert an accent piece of veneer or sand it of and start over. Bummer either way.