"What I had done was set up a checking account in QB called petty cash, and every purchase I made using my own cash (not from the business), I wrote a check for that amount in QB as a petty cash check using the appropriate expense account (materials expense, etc). These are business expenses that I made with personal cash I had in my pocket because I forgot my credit card, or gave someone some money to run out and get something I needed.'
Perfect! Personal cash, personal check, personal credit card, or even paying with Chickens, that is perfect.
"My question is, how do I get that balance to zero? I understand I set it up wrong (I need to get the cash from the BUSINESS checking account first and replenish it as needed),"
No, that is not WRONG and that is a different concept. Petty Cash in this second concept is Transfer of Cash from Checking to Petty Cash Bank in QB, then showing how you spent it by using Write Check, exactly as you are doing now, but Already having money IN petty cash :)
"but I'd like to reimburse myself for these expenses if possible without needing to reenter them as owners equity or something."
You refill your Negative by using a Deposit FROM Owner equity, to show "owner paid." This is your Invested value.
If this is a Sole Proprietorship: You don't reimburse yourself; you take a draw any time. Even if you never spend, you can take business funds, if there is plenty on hand and you want some :)
If this is a corporation, you would not use that Petty Cash owner Funds account concept at all. You would reimburse yourself by writing a Check and listing the things you paid for. They are Buying from You.