I believe that someone added that wood to the underside of your pop-top. Original was the dimond tufted leatherette stuff.
I suggest that you just remove as much as you can and look into foam backed headliner from an auto upholstery supply house. It can be easily installed, but be sure to get the professional glue they use.
As far as adding the laminate, I am against that as it only adds more weight
to lift and support. The boot is fairly simple, same width all the way around and if you make it so it overlaps at the back you can fit it when installing and glue the overlap in back with the proper adhesive. Look for a canvas and awning
shop for that kind of work. I have been quoted about $400 for a new one.
FWIW: The original fabric on my 73 Hunter only needed a good cleaning and new screens and window flaps., about $150
Those loose threads are common. Just sand down the inside surfaces to remove them, put on a good coat of marine fiberglass paint
and go from there. Also be sure to fiberglass over any extra holes that were added.