NFT stuck without gas

Hi,

my account got hacked recently and a bot has been set up to instantly drain all gas sent to it. However, there's an NFT left on it that has significant value yet the attacker seems to have missed it. How can I transfer this NFT to one of my other wallets?

Is there a way to send ETH and use that ETH on the other account to send back the NFT all within one block?