Help identifying differential 65 Barracuda V8

I believe that is a 7 1/4”, and there should be some stampings in the edge of the ring gear to identify the gear ratio. That being said, for all of your upcoming upgrades, you should strongly consider replacing the entire axle assembly with either an 8 3/4”, which would allow you to keep the small bolt pattern if you desire, or an 8 1/4” which will have the large bolt pattern. With the play present in the rear, regular driving will probably not harm it, but with your upgrades, I’m afraid that it will not last very long.
I appreciate that perspective, thank you, and that’s exactly why I asked… I’m taking everything into consideration, im at a crossroads with deciding the future of the differential with the future upgrades in mind…

in exploring the two 8 diffs you mentioned, is there an adapter or anything that could be done to still allow me to run my dads wheels that were on the 7-1/4”? Not to be petty but they are sentimental to him and the story of the car but obviously not a priority over mechanical reliability…

I suppose this also changes my rear brake lines and brake needs… currently 10” drums all around and was just about to order a full replacement brake line kit soon… will this get me in trouble with the driveshaft as well? Will the 904 be able to handle all of this? thanks for the feedback!