Help identifying differential 65 Barracuda V8

Hey FABO! Looking for some help in identifying the rear end on our 65 Barracuda/273 V8. I can’t seem to find a tag anywhere or any other numbers other than what’s pictured.

When I grabbed the flange I immediately noticed some “play” (i have not measured the backlash with a dial indicator yet, this was just a pre-inspection) as I turned the flange, minus the drag on the drums which are still on, there is noticeable play in the gears and I’m not sure where this puts me in the build of reviving my dads barracuda…

I am new and still learning what I don’t know.

As of right now, the plan is going from the standard 2 barrel to a 4 barrel manifold/carb, little bit larger cam, a904 cable auto trans is currently in the shop for inspection and possible rebuild, a 340 throttle bracket and the BPE kickdown cable kit… with all of that in mind and the condition/ potential or lack there of, with what looks to be the 7-1/4 diff… is it worth running and or rebuilding, oil it up and run it? Or considering the rest of the build, does this put me at a crossroads in needing to explore other options ???

There is a soft and final budget for the total build. With this being a crucial part of that build I understand and respect that quality isn’t cheap.

Not looking for anyone to hold my hand, only asking those with far more wisdom and experience than I on what to consider in making an educated decision… any and all feedback is greatly appreciated! Thank you!

(FWIW there was still oil in the diff after removing the cover and there was no metal in the bath or on the magnet. This car was parked for 20+ years)

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