I can't explain why, but the behavior seems to be working as expected now. Even my Smart Mailbox is working properly, and new emails aren't being shunted to the Archive first. I haven't made any adjustments. Since Apple doesn't do background updates (or I should say, I have that feature disabled), my only guess is that Google might have changed something on their end.
This pretty much resolves my issue.
I also thought that I had lost the ability to see my spam folders, but I see that Apple has simply shuffled their location in Mail. Instead of appearing as IMAP folders underneath their respective accounts, they now show up in "Junk."
Edit: Mail also appears to be a bit weird at times, as the message counts don't always match up and respond to your actions. For example, I received 50 messages, some of which were grouped in conversations. I quickly deleted messages until I had about ten left; Mail kept up at first, but then began to go out of synch with me. For a while it indicated that I had somewhere between 20-30 unread messages, even though I was down to less than ten messages. After about a minute the counts continued to adjust until they represented what I was seeing.
The "activity" pane of Mail was blank during this process, but it seems as if Mail's counts were derived from Google's servers rather than what was in the program itself. That's the only possible explanation that I can think of to explain the delays. I'm using a SSD and wasn't straining it, so unless Mail's new database techniques are incredibly inefficient, synchronizing with an internet server (over my crummy DSL connection) seems more likely.