I'd gut it, go with new vinyl and lattice - but do it in sectional panels that you can pull off if (when ) you need to get under them. That's also easier to make than one big piece at one go.
Make a cardboard/butcher paper patterns of where you want the panel, cut that out of 1/8 inch marine plywood. Wrap the plywood in vinyl and foam, using contact cement to make it nice and tight. Double sided tape it to the ceiling and move to your next panel. When the panels are done use mahogany strips as your latice work. Lay it all out with painters tape first, then install it right over the tape if you want.
You can get strips out by ripping a mahogny decking plank up - 84 lumber here in Annapolis sells 5/4 x 6 inch by 20 ft long mahogany decking for 2.29 a foot. At 1/4 thick one plank gets you 12 - 13 (depending on saw kerf) strips of latice from each board. Takes about 20 minutes to strip up a plank, nothing at all. Run the strips thru a planer on one side and you got sweet wood that's easy to varnish (or oil if you want easy no nonsense wood work).
Now If you are really good and handy, do ships laps with the latice work, and make that into panels too so you can pull latice work and panels down with a couple of quick twist (finger) screws.
I'm helping a friend layout the salon of a Islander 37 with this.