Just an idea...
As long as your old--and most likely somewhat grungy by now--carpet headliner is already trying to come down all by itself, why not finish the job and replace it with nice clean vinyl? Easy to keep clean...would definitely update the boat--nobody's used "monkey fur" since the mid-'80s...plus, it would increase the available light and prob'ly increase the apparent size of your cabin by about 50%. Auto upholstery shops have a nice selection of foam-backed vinyl headliner materials and can tell you how to secure it--whether with glue or teak strips screwed into the cabin top (which is a WAY cool look), or both. As the header says, just an idea...