Resolution, so far.
I glued 3 of the panels on this morning, clamped them, and then over a few hours it became clear that I hadn't done it well and it wasn't going to stick long term. Pulled them all off with much cursing and cleaned off all the glue.
Went a bought contact cement, aka fancy extremely smelly rubber cement. Seems to be working so far. Cats are pissed because they can't go in the utility room. Luckily, it's 50 today, because I've got the windows and door open for ventilation and turned off the furnace.
Still have to do the 2 big panels, but realized that I should have put them on BEFORE we drilled through the back of the cabinets for the gas pipe, so now I'm stuck. My very talented friend will be asked to help me cut them neatly, then I will attach the big pieces and the little pieces cut out so it looks better. Oh well, it's a utility room and neither side of the cabinets will be particularly visible.