For doing just that, I bought a few boxes of HP transparency film for HP inkjet printers, and found it not at all satisfactory. I took forever to dry, and tonality was limited, larger areas blotchy. I guess I was expecting something like a big Kodachrome, but that is not what I got.
I also bought a Tektronix color laser printer (about $7000) which did better on film than the inkjet, but still lacked the tonality of what I was getting with inkjet on paper, and tended to be more dense than inkjet on film.
For making transparencies, up to 8x10 or 8 1/2 x 11, we ultimately went to dye sublimation technology, which was costing about $3 per print 15 years ago. Then most of went through the printer were slide prentations usig two solid colors, three at the most, per slide.
My experience with stage lighting tells me that any of these technologies will fade pretty fast for where you are talking about using it. Even getting past "can the film handle the heat" we get into "can dye-based inks handle the light absorption?" Maybe you can print with pigments rather than dyes, but pigments may heat up faster. Incandescent lighting behinds the images just kind of scares me. All the big transparency murals in train stations and on subway cars and busses were backlighted with fluorescent lighting, in the days before LEDs.
Tom Test
Itasca Spirit 29B