Okay, it’s been a little while now and I have updates. I also think I’ve found my solution and, as it often is, it’s a simple one. Here’s a long post if you like details. TL;DR at the end.
If you recall, at the start of all of this I was only getting a 3-3.5 hour burn with my Regency. I was not monitoring the temps at the time, but I could physically tell it wasn’t burning near hot enough. Could not heat the house higher than ~65°F.
I installed the damper. I did not have an in-line thermometer to install, but I have an IR thermometer that I’ve been using. When the air intake was completely open and the damper mostly open, the fire itself would burn at ~550-600°F for ~4 hours, and the top of the stove (where it emits the most heat) would read in the low 500s. This was able to heat the house just a bit better, up to ~67°F. I loaded the stove up with wood, closed the air intake and the damper completely, and let it burn as slowly as possible. 7 hours later I had one little coal still burning away in the stove. Not great, but it was an improvement from before the damper.
Not satisfied with my results, I cleaned the stove again. Really thoroughly this time. I removed all the fire bricks and tried to remove the jets along with the fire bricks up top but couldn’t figure how they came out (a figure in the manual suggested that one wall of the stove needed to be removed to remove the jets. I wasn’t going to play around with that). I vacuumed everywhere I could reach, I used a steel brush to brush the jets the best I could, and I put it back together as tightly as possible. Nothing in particular stood out to me as an obvious obstruction or issue.
I started a new fire. I used a new fire starter, so I layered my starting logs a little differently. I repeated my conditions with the air intake completely open and the damper mostly open. To my pleasant surprise, the fire was able to reach a temp of ~825°F, with the top of the stove not far behind. Huge performance difference. The fire inside seemed much more active as well, and better air movement. I was able to heat the whole house up to 72°F like this, which is plenty warm enough for me. I repeated my conditions to making the burn as slow as possible. I meant to check it after 8 hours, but something came up and I hadn’t been able to check it until 13.5 hours later. Went down to the stove expecting it to be dead and cold, but to my great surprise the stove was still at ~150°F and had a small bed of coals at the bottom. Again, a massive performance difference.
I continued this for a couple of days and noticed that this performance seemed to be steadily getting worse over time. Eventually, the fire returned to capping out in the 500s. I thought that maybe I need to clean this thing weekly? Was that realistic? It didn’t make much sense to me. I spent time contemplating and even spent a good amount of time just watching the fire, looking all around the fire box I could. I noticed that the fire was back to not looking as active as it had right after my cleaning. When I put that into perspective, I noticed that nearly all the jets in the stove weren’t doing anything. But they still looked clean.
Then it clicked: I had gotten into my old habit of layering the logs primarily north-south. It’s easier to load this way and I can really fill the stove up. And it’s lazy of me. However, when all the wood was stacked north-south, all the flames were drawn to the back of the stove, and only reached the jets in the back. The three other sets of jets aren’t being used this way. I tamped the coals down and threw a layer of logs in top east-west. Once they caught, all the jets engaged, and the temp rocked up again.
TL;DR: damper helped a little, and a thorough cleaning likely helped a bit. In the end, it was really just user error. The solution is simply stacking the wood in alternating north-south/east-west orientation. This allows the flames to move straight up to the jets rather than being routed to the back or sides of the stove exclusively. When those jets are engaged, the stove burns much hotter.
It’s only been a day since I realized my silly mistake, so if something else reveals itself to be an influence I will update again. Thank you for the advice, bholler and begreen.