I've been using dissimilar wheels for years. The most important thing is that the loaded radius be within 2% or so. This means you can run any width tire on any diameter wheel as long as the loaded radius is the same (within the 2%). If you do not plan on running the spare for any length of time, but just as a stopgap, then a skinny, 3860 load rated tire, would be fine. The L.R. is computed with the weight of the vehicle on the tire; measuring from the center of the hub to the ground.
You probably did not take into account the deflection of the tread and side wall making the loaded radius more revs per mile.
My factory spare tire, 16" steel 8 on 6-1/2" rim; -8" wide with 6.25" back spacing, with the stock tire will fit between the frame rails on my 2001 Dodge. Anything larger will not. What happened? I removed the factory trailer hitch and substituted a Class V which has thicker steel and more bracing. I get around that by deflating the tire so as to fit between the rails. I've only used it once in 16 years. On the rare flat tire I've been able to use Safety Seal plugs and my 20 # CO2 tank, and a 12 ton hydraulic jack and jack board to do it all without removing the wheel.
I'm in the throes of deciding where my full size spare is going to go. There are basically three ways to go.
1. Deflate the tire even farther and use a tire iron to swedge it up there while someone cranks it up.
2. fab up a front receiver hitch with a spare tire "L" bracket. Of course, you had better have a great cooling system.
3. Do like Alex (ctraveler2) and fab up a rear, swing away tire carrier that also goes into a Class V hitch. This has it's own problems too, but you won't be running hot in Death Valley..
There is one more possibility with a TC that sticks out beyond the rear bumper at least 18". I think (make that hope) I can lay a tire on top of my 20" hitch extension and fab/weld up a plate with 3 lugs for the spare. This would also be a step up to the door.The added plus is it would be like bumper cars at the carnival if some one rear ended you. 8<)
I don't think one size fits all in this regard. If you need a LOT of approach and departure angle, this would be problematic.
I'm sure some of you have better suggestions. Put 'em on the table.
jefe
'01.5 Dodge 2500 4x4, CTD, Qcab, SB, NV5600, 241HD, 4.10's, Dana 70/TruTrac; Dana 80/ TruTrac, Spintec hub conversion, H.D. susp, 315/75R16's on 7.5" and 10" wide steel wheels, Vulcan big line, Warn M15K winch '98 Lance Lite 165s, 8' 6" X-cab, 200w Solar