I also built bridge and engineering TOS playsets out of cardboard when I was younger. I matched the size to the action figures and paused the episodes to make sure everything was as accurate as possible.
I had a friend who did that, reconstructing the transporter platform. Only one minor deviation; he made the "chamber" rectangular! He didn't have the Tech Manual or the ship blueprints and thus never realized from the TV alone the platform was circular. I acted like a bloody schmuck and gave him h3ll for that.
On the other hand. he contructed a "life sized" medical bed readout screen that wasn't too bad. He added a really cute feature. The range "needles" were rigged with strings which connected to two different "rods". Pull one rod and rge readings "elevated". Pull the other and he could perform a "Gary Mitchell" and "flatline" on command! Well, I found it clever.
It reads as though you have some really understanding and fun loving parents. You don't have any photos from that era, do you? If you're concerned about identity, you can use an image editor and blur out your face and any other details that might reveal too much.
Wow, the medical bed readout thing sounds awesome. I'm jealous of that.
And, yeah, my parents were great about Halloween. They loved making costumes and props...although they both more or less hate TOS now. I may have worn them out on it. haha.
And if I can find pix I'll post them! A thread of board members in ST costumes as kids might actually be kind of fun.