Yes, just put it in. Turning it upside down will make it drive backwards, and since the front will try to drive forward, you'll end up ripping your frame and body in half, and that would look silly. That's a low-pinion 60, so you won't have coast-side gear strength problems running it in the rear like you would with a high-pinion axle. 35 spline chrome-molly shafts and CTMs should hold up to most recreational use. The ball joints may be your weakest spot. Is that a CAD axle? Does anyone make alloy CAD shafts?
Running it with the differential off-center could cause some vibrations, if the u-joint angle at the diff and the u-joint angle at the t-case are different. What about picking up a rear 60 from a junk yard for $100, cut the inner knuckles off the Dodge front and weld them onto the rear axle? You'd almost certainly need custom-length shafts, but that would center your diff and solve your potential CAD problem. You would need to figure out a seal, since most rear 60s are full-float and are sealed at the hub. That shouldn't be too hard to track down though.
I'd avoid running a spool.