Bit of a bump! After half a year of multiple print shops not getting it right, refusing to work with me, or ghosting me, I purchased a printer secondhand and printed and laminated the seat backs myself.
The printer is a Canon IPF6450; 12 pigment, 24 inch inkjet. It was a challenge to find inkjet-printable adhesive vinyl media, but I did and it prints great. It's not the nice air release stuff available for latex and UV printers, but if you're careful applying it to the surface it goes on ok.
Expect the artwork scan files posted soon!