I didn't say anything about the wheel, I said tire size doesn't jive with what you seem to be describing. You also haven't given much explanation as to your goals. The bits that I see suggest that you are looking to build something fast, AWD, and moves well on road. I can not see how a 31" tall tire and solid axle will achieve those goals. If I am wrong and you are after the sam off-road then you are.going to want more than a 5" sidewall, even if it means a taller tire. You said sleeper so that sounds like a street rig to me.
On the subject, wheel diameter does not determine tire width.
I said AWD transfer case won't survive mismatched gearing and tire sizes. You never said (in this thread) what transfer case you were planning to use, the only one that Ford built that would fit this description was in the Explorer. Also the hummer may weigh 10k, but the power profile and use case between it and your gas engine are much different. Don't assume that just because it does fine in one it will in the other.
I said a TTB (early ranger) or solid axle will not survive. You said SAS, your hummer example does not use a solid axle. A SAS is going to require a lift in order to clear, which does not go well with what I gather your plans to be. An AWD SAS is not going to steer or handle great on the road. A SAS is going to add a bunch of weight. A SAS was not designed to survive long term in the conditions you suggest to use it, unless you plan to drop $$$$$ on an off-road competition axle, even those get serviced and rebuilt fairly often.