The foreclosure process is set forth by the laws in the state you live in, so they vary throughout the nation. That being said, the mortgage company has no obligation to stop or pause the foreclosure process just because you are trying to conduct a short sale. The short sale is not a "right". The bank can deny the short sale, for many reasons, even if the sheriff sale is months away. The sherriff sale is one of the final steps in the foreclosure process. In most states, there is a confirmation period after the sale that is about 3-4weeks long. The high bidder does not own the home until the confirmation hearing, at the end of the confirmation period, that confirms the sale and the deed changes hands then. So you actually have up until the confirmation to work this out with the bank. But, still no promises! Your short sale contract with the seller is "subject to lenders approval". Although it was signed by both the buyer and seller and meets the criteria for a contract, it carries a different weight, because of the clause, "subject to lenders approval." Check with a foreclosure attorney in your state for more specific advise.
As long as you have proof you are up to date, you will have no issues.
There are Minimum score requirements for every traditional loan, each type of loan (fha, Va etc.) has it's own requirement and each lender, may also have a requirement. You need to speak to a lender and get some advice on your score. If they can't help you, you can look into an "Owner Carry" where the seller agrees to be the bank, for all practical purposes. The seller must have a paid off home to do that. Or, you can look into a lease purchase, which is a rent to own, kind of deal.
Have your Realtor look for, "Owner Carry" homes for sale. In this case, the owner will act like the bank and your credit score is not an issue. The rate they offer will likely be higher, as will your down payment. The terms of the loan can be negotiated out and a good title company lawyer can prepare the Note and Mortgage. I hope this helps.