I found what looks like the perfect trailer for a GT40. It's light weight (~950 lbs) and the GVWR is about 6,600 lbs. It has a fiberglass top that tilts out of the way (no need for hatches for the door) and a tilt bed. But Racing Shuttle 3 trailer is made in the UK by Brian James Trailers. So importing to the US and converting to DOT standards would be a pain and expensive, but if I could find a couple of other people interested in getting one of these trailers, it might make it more reasonable to import a bunch of them. At the current exchange rate, the price is $16,200 in the UK.
www.brianjamestrailers.co.uk
(the tire rack is an option)

Race Shuttle 3 is a mid-sized clamshell trailer - Brian James Trailers | Brian James Trailers - UK
A mid sized aerodynamic clam shell trailer suitable for rallying, club racing, right through to formula series cars


(the tire rack is an option)