One year after posting this question, I've finally resolved my issue so I thought I would answer my own question to share where the journey led me:
Step 1: Try Replacing Cartridges
As HoneyDo mentioned above, the first thing I tried was to replace the faucet cartridges. The tub didn't work when I made an offer on the condo, and I had a plumbing inspection completed at the time: Replacing the cartridges was the suggestion from the plumbers. The quote for this was $300 and it took me less than $50 and about 15 minutes to do the replacement myself. This did not fix the issue. I might have been able to do this for free by contacting Moen for the cartridges (I heard they provide lifetime warranty), but I didn't think of that.
Step 2: Try Replacing Rough-In Assembly
The specific faucet I have from Moen is installed with a pre-built rough-in assembly made out of copper. I thought this might have been clogged, so I purchased the assembly on Amazon and installed it. This was a more expensive and difficult DIY task. I have Pex pipe and so I had to solder the pex adapter to the copper rough-in assembly and then crimp the pex to the adapter. I didn't have the tools for this, so after renting a crimper and buying a torch, the adapters, fittings, and rough-in assembly, it cost about $300 to fix and took me about a day to learn everything and get it done. This also did not solve the issue
Step 3: Try using air pressure to dislodge the clog
At this point, I realized that the issue I had was not accessible near the tub so I starteds to think it must be an issue in the pipes themselves. Rather than tear apart sheetrock to access the pipes I tried to use air pressure to release the clog. Basically, I plumbed a three-way assembly with 1) hot water incoming from clogged line with shut-off valve, 2) Compressor adapter for air input, and 3) valve with hose adapter. I then pressurized the line with air and turned on the water, and opened and closed the valve over and over again. This helped and increased my water pressure, but was not enough.
Step 4: Think about any Devices that might be installed on the water line!
This really should have been step 1 for me, since it ended up being my issue. But after talking with a number of plumbers about my issues, I'm convinced not many people would have thought to look for this: My tub has a thermostatic mixing valve (TMV) installed for the hot water line. This was not located in my bathroom, but was behind an access panel in my master closet. The device mixes cold water with the hot water to avoid scalding bathwater temperatures. In my case this had become fowled.
Step 5: It might be time to replace pipes
I actually came to this conclusion after step 3. I came across the TMV only by cutting holes in my ceiling to trace the hot water line to the TMV. When I found it, I was relieved that I wouldn't have to replace the pipe, but also bummed that I could have easily replaced the TMV without tearing apart my condo. But if I hadn't found the TMV, replacing the pipe would have been the next step.