
Hi Fairplay,
You have discovered a problem that many other boats suffer from and headlinings can be a real chore to sort out. If you get to the stage where you remove the headlining then you are met with all of the degraded foam and backing material; not good at all. My 1990 had 'slack' headlinings in the forward cabin and the midships bedroom/cabin, which I pointed out to the broker. As it was one of their stock boats they got there interior man to have a look. He has installed on either side of the headlining where it meets the side trim some neat stretcher strips that resemble small plastic cable trunking. In so far as how he did the job I can only imagine that he had a helper smooth the lining towards the edges and then screwed up the trunking. It certainly worked and although the lining is not as Fairline intended it is acceptable to my tastes and I'm a 'fussy bugger'.
There is a picture of another 30/33 Tri-cab on Google Images that clearly shows a headlining fixed by many capped trim screws (like number plate screw fixings) I think it makes the looks very 70's/80's pub interior
The alternative that I had considered (but have not yet done...not needed yet, but i like to have more than one arrow in my quiver) is to remove the lights and using a longish tube attached to an aerosol contact adhesive spray and squirt the adhesive around between the underside of the roof and the topside of the lining then using a 9 inch paint roller smooth the lining back into contact with the roof. You will not have the foam to give a soft feel finish as it has degraded but the lining will be stuck and not hanging down. Some may say this sounds like a bodge but it was stuck up originally with glue so who is the bodger. The Tri-cab Targa is a great boat and really comfy, I have come from a Princess Flybridge to the Targa and have not regretted the change.
As far as I can make out at manufacture the lining goes in and then the cupboards are fitted so the lining is between any woodwork making removal a real chore.
You might get some useful info from some of the coach trimmers that advertise, or go to one and sound them out for info

Good luck