Well. Issues solved, or at least a whole lot better now!
And despite causing myself some embarrassment, I will detail what the fixes are.
First, I disassembled the feedhorn from the LNB and inspected it. There was some dirt built up inside. I thoroughly cleaned all of this and reassembled. This didn't seem to improve things any.
Next, I got the bright idea to try one of my cheap Chinese universal LNBFs. It fits the mount, and is much less heavy so it's not trying to fall off. Also the throat of the feedhorn is not nearly as long and a little wider, which translates to a lot more tolerance to having exactly the straight look angle. I was able to adjust it for best signal and it's actually pointing slightly downward. This improved the signal around 5% or so, but for the size of this antenna I still didn't feel like that was enough improvement.
Finally, I got to the literal root of the problem. I've been using a satellite finder app on my phone which does an AR-like view of the southern sky showing me where the satellites are supposed to be. Instead of relying on this, I decided to actually measure the angles more accurately and what did I find but a heavily leaf covered tree limb in the way. So I got out the post hole digger and moved the whole thing about four feet forward and planted it. Now my signal is significantly better, was able to tune it in on Alex Jones' ridiculously weak transponder quite quickly. He, and the national and Montana PBS are coming in quite well now. I'm still not seeing the Family Radio mux (11993V1075) however.
As measured by my receiver for that specific weak transponder, I was previously getting around signal=65, quality=60, now it is a steady signal=77, quality=70.
Thanks for all the help and suggestions! Especially all the stuff about theoretical and pictures and the angles.