There’s no shame in a nice plywood patch, as long as it’s temporary.
Plastic probably isn’t a great long term solution anyway, unless you have a handy neighborhood Tap Plastics… those are large panels that need to be cut from a big sheet. It’s probably acrylic which starts out fragile and just get more brittle with sun exposure, cleaning chemicals, air, etc. ;-)
You could try to replace them with polycarbonate but I’d check on the price of getting some glass cut and laminated. You could even just turn it back into a window. Definitely seek advice on how to “reglaze” the windows from YouTube…
I tried to substitute modern silicone caulk for crummy window putty once. Then I cracked the glass and spent a week scraping out the very tenacious caulk. Turns out sometimes the old ways do work best.