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I would be really curious what you come up with for the spare tire mount in the cab. Kinda hard to see how 37 will fit via rollbar/clamp/dom mount. My situation is a little different cuz I have a "trunk" structure that is ~5" above the actual floor. I built a very simple, but similar, mount to what you are thinking for longer trips using dom and flatstock to mount to the tub threads where the hard top mounts. One downside to this is I can only use it with soft top cuz with the hard top on I can't physically get the mount IN the jeep.....and obviously can't put the hard top on with the mount already installed. The problem I'd see with rollbar idea is that the tire is just too large. I even had to install an Excessive Industries "40 bar" to replace my rear cross-member to get a tiny bit more clearance.
Picture off their website with a 40. Mine ended up looking similar with a 37 cuz of my "trunk".
Anyhow, you have a great build thread going and I'm really interested in what you come up with for a spare mount! Maybe you're thinking of it just being a top-off thing??
for what it's worth, with the introduction of GlueTread, unless I'm on a multi-day overland trip I no longer carry a spare tire on the trail, and instead keep it at the trailer/camp. Being on 40's this has been especially helpful. GlueTread is basically a tire repair kit in a bag, and is exceptionally durable - plenty enough to get off the trail, or home.
However, for multi-day overland trips, I'll be fabbing up a swing-away tire carrier outside the back end - much like the EVO, DV8, and GenRight carriers, that swings open same as the tailgate...