Great question. I raised this shared concern with @dave and he advised that the Burke 115 can accommodate a fiberglass no-cut cushion set, but that there's no known way at present to avoid cutting into a Burke 116.
A lot of people probably just accept that as the final answer or weigh the merits differently.
I definitely want to study this further on my other Burke 116 chair and determine if I can see how that could work. I have a few ideas in mind for developing courses of action in the cushion mating area that without a visible difference reduces cushion material thicknesses instead of the fiberglass. TOS prop-makers probably didn't have the capabilities available back then or were simply under cost and time pressures to develop alternatives, and just cut into the chairs to meet the show's scheduling deadlines.
Without having the cushion dimensions to work with it's all expensive guesswork/trial and error to find a way to avoid cutting into the Burke 116 fiberglass. I'm pretty sure it's going to save time, energy, and money in the long run for someone to go to the trouble and take accurate, reliable measurements.
It has been noted the angst of Burke 116 chair prop-makers about having no option other than to cut.
In support of efforts to find ways to do things differently that will work just as well, I am putting in an order for Polytek's 74-30 polyurethane and some thickener to take castings of the chair buckets, pedestals, and memory return mechanism pieces. At some point future, run each of these items through a 3D scanning arm, import the dimensions into Autocad, 3D printers, etc., and also just upload this information for the benefit of everyone. The good thing is once it's done, it's done. The captured dimensions are always there.