If the appraised value is $350,000 the bank may want to get closer to that amount. You have to decide what you feel comfortable with as an offer. Test your counter offer since it is likely that the company will make a decision on your offer before moving on to a new buyer. I have had at least one short sale where the bank was willing to give on seller contribution so its possible they may agree.
Note, however, that with a short sale, the bank has determined a net amount they expect to receive. Don't fight the bank over the $350,000 just because you feel as though you should get it lower than the asking price.
Millie C Lumpkin, CDPE, SFR
Keller Williams Preferred Realty
Orland Park IL