Trying to get funds to Matic without any Ethereum in my wallet

I know this is a noob mistake, but it's an especially expensive one on Ethereum. I purchased some Matic on Binance and trying to transfer it to Matic network. I should've listened to the guy who suggested going through BSC but selling and rebuying Matic again seemed like more work initially (although in hindsight would have been probably easier). So I paid ~$20 to Binance to move my Matic to ERC20, figuring it would be a one-time fee that I would quickly recoup with some yield farming on Matic. I knew the bridge would cost me another $10 or so but didn't realize I could only pay that fee in Ethereum, which I don't have.

Now I'm in a position where I can't even buy Ethereum with my ERC20 Matic because swap fees are in Ethereum as well (I need ~$1.7 to approve Matic/Eth swap, and then I figure another couple bucks to trade it). Moving more money to Binance to buy some Ethereum to then send it to my wallet again would probably cost me another $50 in fees or so. What are my options to get the $5-10 in Eth I need without paying another $50 to get it to my wallet? I do have about $100 on Matic network if it's possible to transfer any of that to Ethereum for cheaper?