After you file

The longer you wait the more interest you owe on your outstanding balance.

I called the IRS amended return number and asked exactly this question.

 

The IRS person, who seemed competent, said absolutely, file the amended return ASAP.

If you don't like that, at least pay what you owe now via IRS direct pay.

Meanwhile the UCE refund is being calculated outside of the amended return pipeline by  a separate computer system.

 

Use your own judgement and common sense.