From my experience, banks are not that naive. They don't really fall for " gimmees" . However, to your point, I would work hard on showing the bank why they should take your offer.
For example, submit photos of any signs of distress on the exterior of the property, the interior, the neighborhood, etc...Give them every reason to do your deal. They don't really know what is going on, so paint a clear picture for them. In addition, don't be afraid to give your agent a helping hand. If the agent has allowed a short sale to sit on the market for 100 days, then that is a sign that they do not know what they are doing.
Help them gather market data to submit to the bank that shows your offer to be compelling. The bank is particularly interested in working out " fair" or " compromising" , they are simply trying to mitigate risk. Without the right data, they will assume that owning the property is an acceptable solution. It is the agent/investor's job to convince them that they do not want to own it.
Good luck!
By the way, you might want to remind the realtor that it's their duty to submit all offers.