Yes. new Bittrex account.
You will have to become ENHANCED verified with both accounts. When you do the enhanced verification with the second account (using the same telephone number and showing the same government ID) they will automatically block the 2nd account. Then you need to open a support ticket to notify them of MULTIPLE accounts.
It takes a while (about a week) for Bittrex support to allow/authorize the multiple accounts.
Then you can generate new API keys from the new account and notify Gunthar. He does *not* charge more money for multipel APIs at the same exchange.