No. People quote the nominal size of the ring gear as a "name" cause differentials don't generally get alphanumeric code names like a transmission or an engine. But something listed as a 7" is gonna be for a GM axle, not the Mazda unit. Pinion and carrier bearing sizes along with (shims for those bearings) will be all different across almost every manufacturer.

You can stop wasting time searching, there is no kit. Mazda doesn't sell one. Nobody sells one. No such thing as a "universal" kit. You will have to buy individual parts like at the link I posted above.

Pages 19 and 20 of this pdf detail the pinion height measuring tool and reference a part number, but I do not know if that is available for the general public to purchase;
http://www.mellens.net/mazda/Mazda-M...fferential.pdf

Upon closer reading of that pdf, even the Mazda directions state to reuse the original shim. Just do that and 99.9% chance it'll be fine!

Darn, alright. Well hopefully it works! I don't see why swapping something that is the same size would require new shims but the professor swears up and down that I'll probably need new ones.. Alright thanks guys! We will see how it goes.

Show them the FSM, let 'em argue with Mazda ¯\_(ツ)_/¯

I see "FSM" but what exactly does it stand for? Haha but yes I will do that
Oh just kidding I figured it out haha. Thanks for all the help guys! Really appreciate it!

"Factory Service Manual"

Factory
Service
Manual

The more you know