When I try to make an overriding transaction in Sparrow it tells me I don't have sufficient funds when I enter the Sat amount of the competing transaction.

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That's even if you choose a lower amount to send?

Yes

https://github.com/sparrowwallet/sparrow/issues/530

I wonder if this operation via RBF is still available in sparrow.

The weird thing is, when I look at the transaction in Nunchuk it is showing that it was signed. How is that even possible if I need to sign it with an air gapped wallet like my Cold Card, including writing the transaction to my miniSD and signing it with the physical device?

If you succeed in moving your coins, definitely send them to a new wallet, not to an address generated by your current one.