Wells Fargo and BOA are two of the highest respected lenders out there. If you can show you are sure to qualify for your loan, along with the other Short-Sale Required documents, you will have a better chance then someone who is not.

Hi Katie, switching lenders may make a difference in the eyes of the Short Sale negotiator as some feel that a retail bank has a better ability to close the loan. I would say that the structure of your offer probably carries more weight, however. The market mentality of Sellers/Short Sales/REOs has changed from “best price” winning deals to “good price with highest probability of financing and closing.” To this end, the larger the down, the more secure the seller feels. Even if you do these things, knowing whether the timeline will be shorter is still a big unknown, unfortunately.

Ask your agent to ask the listing agent for advice on these topics as the listing agent has access to the negotiator, and therefore, what the lender has been accepting.

Best, Steve

Katie, Waiting for approval is the hardest part of the entire process. If you are completely preapproved with a reputable lender and have provided documentation that you have been credit approved, employment verified etc. it should make no difference on the short sale approval who you obtain your mortgage through. If you have not been through a complete process of preapplication and approval you should do this immediately.
It is not unusual for a short sale approval to take a few days to a few months for approval, a counter offer or sometimes rejection if there are multiple offers.
A good deal of your waiting period will involve not only your information but the seller's documentation of hardship and application for the short sale. There are many steps involved in granting the seller the ok that the lender will accept less than what is owed on the property and lender will take time to investigate all possible fees and charges they will be paying in addition to accepting the lower payoff.
If this home is a really great potential for you.. hang in there and wait it out :) But do keep up with other possible listings for back up just in case. Best Wishes!!