There are 3 guys who came over from Mesa in my class at Skywest. Based on what I've heard from them, you'd be better off anywhere else. This includes flight instructing and 135 freight. Search the Mesa threads on this forum and you'll find similar opinion.

If you can't get on with any other airline due to your experience, I would strongly suggest you consider flight instructing to gain the experience you need. There are some killer CFI jobs out there right now - a good way to save some money before your first year as an airline pilot.

Don't worry about who uses a QRH and who doesn't until you're hired. The company you end up working for will train you to use their resources. For the sake of yourself and of the industry, I hope that company is not Mesa.