Convertible tops are not that mysterious. (Unless it's a high end German car or something like that)
I have done several with no problems. I almost completely removed the top from my 69 300 at the rear to do the needed metal repairs on the Dutchman panel. I changed the plastic window that came in the car to a glass one and it went back together just fine.
My girl friend has an 05 Mustang convertible and neglected to secure one header latch two years ago. Well..... 65 MPH and guess what happened........ Bent the heck out of the top frame when it blew up. I located a complete top and frame from a wreck.... and swapped the entire top. I had to remove both covers because her top is black, the replacement was tan. It took me 1 1/2 days in the back yard. No special tools needed, just a good drill and rivit gun and stapler.
Some things to concider..... Top replacement should include refinishing the top folding frame. A trim shop won't do that good a job on that, you need to do it yourself to be happy with the outcome, (or a pro restoration shop, very expensive). I would recommend dissasembling the frame, (take lots of pictures), and having it powder coated. Not sure about 66 but rule of thumb for the era was black frame for black tops and white frame for white or other color tops.
Choose a good quality top from a reputable suppler, (Legendary, or google dealers. Avoid Year one).
Will likely require all new seals also.
To have a trim shop make a custom top will run around $1000.00