Can I retrieve funds in a derived address with a high index? I sent funds to a derived address, but I didn't know about the gap limit and how the addresses should be used incrementally. I've used a huge value for the index but wallets only check the first few values -  is there a way I can retrieve them?
Yes, just use something that lets you generate addresses with a high index. For example, you could use https://iancoleman.io/bip39/ and enter into the starting from index box the index you would like to begin deriving addresses at. Then you can get the private keys and import them into your wallet.

IIRC there is not a wallet software that will let you specify where to start deriving addresses.