Have any of the stories been published separately in well-known literary journals or magazines? Have any of them placed in a contest? If so, this might be enough to get the collection "in the door." If not, it's an avenue you might want to consider before seeking representation and publication for the entire collection.
You are right in that this is an altogether different beast from the traditional novel. There have been a few writers who have had breakout success with novels that were actually short story collections (two that come immediately to mind are Sherman Alexie's The Lone Ranger and Tonto Fistfight in Heaven and Louise Erdrich's Love Medicine) but as far as I know, in both cases, excerpts from the books had already appeared in major magazines and had garnered attention. Alexie was fortunate enough to have had a previous book of poetry reviewed by The New York Times, so agents already knew his name.
There are a lot of legitimate contests for short story book collections for which the prize is a publishing contract. They are not usually major publishers, but very respectable smaller houses that will still give a writer's career a respectable boost.
These are just some suggestions that might increase your odds of getting picked up with a short story collection. Good luck.
