I see this was posted a while ago, but I figured I'd share my advice in case anyone in the future comes across this and wants some guidance. I'm currently in my second year of my gap between undergrad and grad school and I'm starting a masters program in the fall, so I'll tell you what I've been doing.
I'm not sure if you're familiar with them, but the Paideia Institute for Humanistic Study has online Latin and Greek reading courses you can look into. They're not free ($200 per semester for a regular reading class, $1000 for an intensive course), but they would be much cheaper than a post-bacc would be and they've served me rather well. Class sizes are 5 people maximum, so you'll get a lot of attention from the instructor, and the reading courses meet once a week for an hour, usually during the evenings, so it shouldn't interfere with work too much.
If there are any Catholic high schools that teach Latin nearby, reach out to some teachers about tutoring. It's good teaching-related experience, it'll help solidify any beginner Latin concepts that you've managed to avoid fully understanding, and it can be good money on the side of whatever else you're doing.
I know OP said they don't have any universities with Classics departments nearby, but if anyone else does, but doesn't want to pay to audit, just email a professor and ask if you can sit in on their class. Some professors might not go for it, but, in my experience, Classics professors love having students in their classes who actually want to be there and who will freely participate. Just give the undergrads a shot at answering before you raise your hand and you shouldn't run into any problems. You won't get a transcript, but you can talk about it in your SOP. Who knows, if you do it for long enough you might even get a LOR out of it.
I was also encouraged by one of my professors to attend any conferences in my area I could and, if you have a paper from undergrad that's particularly good, you could try submitting it to journals that accept papers from people not currently enrolled in a program (there are a few I think, I forgot which ones they are though)
I hope this helps!