Would checking the engine vacuum be a way to see if the exhaust/cats are clogged? I'm using the Torque OBD2 scanner and can see my MAP sensor reading.

 

I'm an old school mechanic with a mechanical vacuum gauge, and yes, a vacuum gauge (or the converted reading for the MAP sensor in kPa or PSI) can be used to diagnose exhaust restriction.

With engine running, in neutral or park, with A/C off, lights off and no other loads on the engine, hold throttle steady with tach at 1000 RPM's. Note vacuum or MAP value at 1000 RPM's unloaded. Slowly open throttle until the tach is at 3000 RPM's, hold steady at that engine speed and note vacuum or MAP value at 3000 RPM's unloaded. The vacuum reading (inches Hg) should be higher, or the manifold absolute pressure (kPa or PSI) should be lower at 3000 RPM's with no load than at 1000 RPM's with no load. If the vacuum reading is lower, or the MAP reading is higher, the engine is working hard to meet the load to push the exhaust through the restriction.

I can't remember if it was Torque or CarGauge that actually has a "vacuum gauge" available which is supposed to show inches Hg from whatever PIDs are available on your vehicle. That would be handy, and the one I saw that on was fairly accurate to my vacuum gauge in a Chevrolet Pickup with a 4.3L V6. In another vehicle, the "vacuum gauge" on my tablet was wildly off from a real mechanical vacuum gauge.

 

Here are my findings:

at 1000 RPM - 21 Hg

at 3000 RPM - 20 Hg

When letting off the throttle from 3000 back to idle, the vacuum spikes to 25 Hg before settling at 20 Hg at idle. If I increase to 1000 RPM from idle, I get back to 21 Hg.

Assuming my MAP sensor readings and Torque are accurate, does this indicate that there's too much back-pressure in my system?

I have the California emmissions (small and large catalytic converters) and what I'd assume stock cat-back. Though I live on the East coast and the car was originally from NY. The Larger cat has definitely been replaced at least once, I can see where it was welded in.

Where could the obstruction be? The Pre-cat, the larger cat, or the stock muffler?

I'm trying to justify buying the Walker 50542 and doing the swap in my driveway versus getting the Walker 81923 and letting a muffler shop swap it in. Both solutions would be about the same money with maybe the weld in being a little less expensive.

 

Sounds like you have some type of obstruction.

Without further testing (checking back pressure with a pressure gauge at the O2 bungs would be the first step), it's hard to say where the obstruction is. It could be anywhere in the system.

When I see welded in, aftermarket catalysts, I always suspect those first. Two reasons for that suspicion. First, the vehicle obviously has a history of destroying that cat. Also, the cat from the vehicle manufacturer is made to meet a very long, very high mileage warranty (8 years/80K miles). That's the minimum warranty mandated by the government for new cars. No aftermarket manufacturer even offers a similar warranty, so the aftermarket cats aren't made to last as long as the factory parts. If I'm looking at a used vehicle, I knock $150-$300 off my offer price if I see non-factory welds around a cat.

I've had really good experiences with Bosal catalytic converters on older vehicles from US makers. Bosal also makes a "for California vehicles" catalytic converter assemblies with Federal (not CARB approved) cats for people in your situation (CA emissions vehicle outside CA and NY). That's a feature that should make the Walker 50542 setup a breeze to install as well.