with LTTP. If you've polished this baby and you're getting requests, then I think you need to submit it to the very end of the line. That "line" may include a small press at some point, however. If the querying process is wearing you down, take a short break and just write for a while to remind you of why you're doing this. You should be writing that next book anyway.
You know, the short story lit mag market works in a similar fashion-- You write a good short story. You send it out to a kazillion places. You received a lot of rejections and a few "almosts," but those "almosts" also comment on the quality of your writing and tell you they'd like to see more of your work. When you have another story ready, you send it to the "almost" markets first, and often, that leads to an acceptance.
Acceptances are like parking spaces. You only need one.
Agents are the same way.