I did (well nearly done!) the same job as you - and starting with the same (Vinyl over old thin ply).
My view is that headliner doesn't really need any protective finish - just cosmetic. My basis for that is that most boats I have come accross have various types of uncoated softwood and / or thin ply above the waterline (and in the interior!) in non-structural places and it is only when unexpected water
ingress happens over an extended period of time do problems occur.
But I still coated mine back and front! (would not have bothered with the backs if the fronts did not also need work).
The original plan was to recover with vinyl (it had both discoloured and in places drooped away from the board), that plan then got changed to replacing entirely with sheet plastic and finally changed to good old fashioned paint!.....that required a fair bit of effort in the preparation, including filling and sanding
(as well as bunging up a few screw / fitting holes for things long gone). A PITA but the panels were simply too good to replace. In addition, I modified the panels (cut 'em in half!) so that 3 panels reaching from port to starboard became six that met in the middle - that mostly so I could get 'em home easier!, plus makes dropping a panel if access later required a lot easier. Helped of course that the edges of the panels are all hidden by varnished wood trim!
After a couple of coats of decent primer a coat or 3 (I forget!) of white paint really came out well (and better than I expected!). Looks like painted wood (which it is!), but in keeping with the overall look of the boat (built in plastic, but in 1970 not 2012!)..........and I reckon good enough (and long lasting enough) for another 40 years, even for 10 years of that will be someone (else!) looking at them and saying "they could do with another coat of paint"!
This thread reminds me that I have to refit
the aft cabin