I'd be fine switching wallets to something that works, but I have no idea how to go about that. Especially if I can't access my wallet to begin with. Am I just screwed if I can't get into my Bitcoin Core?
Not if you have a current backup of your wallet.dat. You can then import your keys to just about any other wallet then, although for some types you may have to use a tool such as pywallet to change the import format.
Another option is to simply downgrade to the last version of core that worked for you until the issues are resolved.