California motor swap stories? I might have a couple, hope I'm not too late to the party.
I lived in California until enlisting. My favorite headaches were due to a built B20 V-tec in my 94 civic. Total sleeper, stock intake and exhaust. I was pulled over once for an exhaust leak, cop said my car sounded modified and made me pop the hood. The build was almost entirely an OEM Honda Frankenstein so I was let go(to the surprise of everybody at the meet) when he couldn't identify any aftermarket parts, even though it was a different series engine. I've had friends with stock engines get basically the same stop but get sent to state ref for having an AEM intake with CARB sticker, the exact reason I kept everything as stock looking as possible.
Every 2 years I had to swap in a stock motor for smog. I basically had to trade motors with a friend for the weekend so they could know what it's like to have a quick car, there's a fun story of my engine bursting into flames in a friends car but that's another story and entirely because my friends are a-holes. 1 year I had a shop owner who said he'd ignore my non-street-legal setup and just test another car with my info punched in. BUT, he offered a pre-check to see if my motor had a shot at passing emissions, he accidentally(?) hit the "test" button and when my car polluted 1000% more than allowable it was red-flagged and now could only be tested at a "test-only" shop where they tend to be a little more uptight. Even after I swapped in a freshly rebuilt stock engine running super clean the test-only shop failed me because timing was advanced a couple degrees too far, I clocked the dizzy and spent another $65 for a re-test. They shoot timing and write it in by hand, they could have let it slide but they preferred to rape a working teenage college student out of his hard-earned money. This experience was my last time dealing with smog. Joined the army, sold the car. When I got back to the states I bought a 75 280Z to avoid smog, wouldn't even consider buying a 76.
Anyways, I'm still on Active duty and have never been questioned about my California plates in Texas or Georgia. Never questioned about not running a catalytic converter in my Z in California so you might be ok with your loud exhaust. I'd advise you to keep your car registered OUT of CA for as long as possible. I only keep mine registered there because I don't want to go through the hassle of registering it from out of state if I ever move back. Since you're going to WyoTech you might have a good chance at finding somebody knowledgeable about if there is a legitimate way to register your Z, but since it's a 76 with a V8 it might be a PITA. You might have to find somebody with a stock L28 and trade for the weekend.
And just throwing this out there, my little brother bought an old Celebrity in Idaho and drove it around CA with Idaho plates for a couple years before registering it. Good luck.