If anyone's wondering, I did notice a minor thing that's not-entirely-related-to-my-system:
As long as I did things like this, I have no problems:
Go to All Topics.
Right click and open-in-new-tab any thread I want to read (by right-clicking on the blue 'unread-message' arrow on the far left).
Read whatever tabs I have open.
See something I want to reply to.
Open reply (in same tab thread exists in my browser, not a new-tab this time) using message's direct reply-to-specific-post button.
Make reply post text.
Usually click Preview button a few times.
Using my all encompassing knowledge of everything, my reply is perfect and I complete it successfully at this stage.
Click Submit Reply button.
Reply posts... and everything works great.
However, if I do this, then things mess up:
Go to All Topics.
Right click and open-in-new-tab any thread I want to read (by right-clicking on the blue 'unread-message' arrow on the far left).
Read whatever tabs I have open.
See something I want to reply to.
Open reply (in same tab thread exists in my browser, not a new-tab this time) using message's direct reply-to-specific-post button.
Make reply post text.
Identify that I'm stupid can't remember what I'm replying to somewhere else.
From the same existing tab I'm in (currently with reply editing box open) I right click on the thread name near the top where all the blue text with -> arrows is. Here, it would be the text saying "Stile's Stupid Test Thread". I right click on the thread name and open the thread in another new tab. In that new tab... I re-read the thread, perhaps look at some message-that-I'm-not-specifically-replying-to, maybe copy some text and paste it back over into my reply-tab (still open).
...this is usually where things go wrong.
Might click Preview button or maybe I'm super-confident and jump straight to the Submit Reply button...
...but post never posts... I get the errors I'm describing above and I generally have to post somewhere else, and/or restart my PC to correct the problem and go back to normal.
This isn't something new, either. This is how I've replied to threads for years and it's always worked with no issues in the past. I'm just seeing this strange-ness recently.
Anyway, I'm fine just not-opening-the-existing-thread-from-my-reply-tab and I don't seem to run into the issue any more.