Very interesting topic! The ST:III/IV era Excelsior always interested me. For the purposes of your project, I hope that you not let any perceived clearance issues with Space Dock doors affect your calculations.
I have suspected that the shot of Enterprise clearing the space doors was framed in such a way to make the clearance look tighter than it really is in order to play up the drama of Scotty barely getting the doors in time. I don't take it that seriously as an objective measurement.
A couple things in this shot can support larger space doors:
First, the space doors may not be completely open. In this shot, you can see that the edges of the doors still extrude from the frame. While it seems apparent that this is as far as the doors open, a possible in universe explanation is that Scotty only opened the doors JUST ENOUGH for the Enterprise to slip through, as a way to slow down Excelsior's pursuit. Excelsior would then have to wait a few more moments to have dock control fully open the doors to allow exit (or fly "sideways").
Second, the shadow cast by the enterprise is below the door frame to the left. I would need to see the actual sequence again to be sure, but from the picture it looks like, contrary to the appearance, the Enterprise is now some distance from the doors, and appears larger because of the perspective. This could allow for the Excelsior to clear the doors.
This is complicated by the fact that the enterprise model never actually passes through the doors -- all the elements had to be filmed separately and composited together. Given that this was made in 1984 on a tight budget, I am inclined to give filmmakers a "bye" on scaling when there are overlapping moving elements. For scaling purposes, the static shorts of the Excelsior and Enterprise carry more weight for me personally. YMMV of course.
That being said, I am very interested to hear what Mr. Probert or Mr. George come back with.