I handle a ton of sales with HUD partial claims. Over the last 4 years they have been giving out these claims like candy to make their Covid workouts possible, and sellers are always surprised at the amounts owed. You can never get the partial claim reduced or forgiven. They must be paid in full.
You have two options: Pay the partial claim off out of pocket or do a short sale. In a short sale with a partial claim, your first lien position with the FHA loan takes the loss so the claim can be paid in full. Currently FHA is offering no doc short sales through 4/2025, so you wont even have to provide any financials to get your short sale approved. Just a standard borrower hardship form. Pennymac is one of the better lenders to work short sales with right now. I have done a few FHA shorts with Pennymac over the last year, and you are looking at maybe a month or two from application to approval, if the person handling the sale knows what they are doing.
However, you would have to rework your current contract to be subject to SS approval (which the buyer may or may not be into),or sell to another party, and if you are getting financing for the new house, that will likely fall apart as well.
If you have the cash to complete the transaction as is, I would recommend simply paying the balance.