Hmm..mushy spot could mean a prior water intrusion -which could also explain why the new carpet was put in. Let's hope that is not the case. (And even if it is, it's not the end of the world by any means.)
Some carpet has a woven, canvas-type backing that gets stiff and "crunchy" for lack of a better word. That wouldn't account for the mushy feeling, I wouldn't think.
I don't really know how the cabover/cap is attached on a BT. There's an old parts catalog on line (different year) but it's over 100 pages and I haven't flipped through it to see if it would be useful in finding out about the connecting bolts.
Likely you've already seen it, but in case you've not: http://dealers.gulfstreamcoach.com/dealers/pdf/2003%20BT%20Cruiser%20Parts%20Catalog.pdf
So when's the first trip?