I street raced a Newport with nitrous on it. No reason not to use a C body for racing, especially if you tweak them a little towards that purpose. As for rears - the engine you run has the potential to break and ben parts downstream. I think you're right to be worried. It's always a combination of power and weight that breaks rears. You have both. It's a toss up as to which will happens first: the axles will twist (may not break but you find it hard to pull them out of the differential) or the housing will bend (as in each axle flange trying to move forward). If you have the rubber isolators on the rear leaves that might save it for a while although you're losing R/T and 60' ET with them.
On repurposing a Dana 60 - Cal Tracs replace the pinion snubber so that's a non-issue if your choice is to keep them. That means any D60 will work. A truck unit will have what you need but you gearing will go up to 3.54. I do not believe there are higher (numerically lower) gears available than 3.54s. All truck D60s have full floating axles and passenger car brakes or wheels will work on them. So you will have to cut off the truck housing ends and replace with passenger car ends, and replace the axles themselves. You can't "fix" a full floating axle to be a passenger car. When you're done, unless you have the fixture yourself, you will have spent within a few hundred of a brand new, custom made D60 with any gearing and new limited slip diff, and possibly new upgraded rear disc brakes. If it was me (I will be doing this for my '69 300 when I get to that car) or if you were my customer I would just order a new one from Dr Diff. You will need to address the driveshaft length for this swap too so budget for a new shaft or modification of your factory one (I would upgrade to a stronger driveshaft and better joints - you've got a lot of torque vs. a lot of resistance to overcome with that car).