I've never made the comparison, but it's possible the standard cymbal stand wing bolts are the same thread size as drum lugs.. you may be able to buy a couple or a pack of them at a music store and if that studio kit frame is like the DM10X frame, you may be able to get away with replacing the lug from the single end of the joiners.. I find if I need to make an adjustment to my frame I can usually get away with loosening just the single lug side of each connector and then swivel the frame where I want it, then tighten that lug up again...
so if your frame connector pieces have three lugs, two on one end and one on the other, try replacing just the one and see if it allows enough give to swivel your side frames inwards (I'd swivel one side in on the inside and the other in on the outside, you may not even have to raise or drop the toms if they happen to snuggle in above the frame or below it when it is folded up, or may only need a minor lift or drop).
I used to have a smaller kit at a friends and he also had a little 2x3 nook and we'd fold the kit up easily like an S (Z?) and I'd just tilt the toms one way or another and it came together really nicely.. even with the lug bolts I'd just loosen one of them and it would pack away in two minutes.