Military flying
It is something that you should at least consider, especially if you can get a slot. Applying to the airlines as a military pilot is virtually certain of vaulting you in front of the hiring line.
FSI has given you a decent foundation (I know; I instructed there), but, if you think that FSI was tough, wait til you start UPT.
Not only does military flying give you great experience, training and background, just making it through OCS and UPT is validation in and of itself that you are airline material. It was explained to me once that a big reason why airlines like ex-military pilots is because the military process does the airlines' hiring screening for them. It makes a lot of sense, because you learn in the military discipline and how to receive and execute orders. Moreover, military flying units are among the best airline networks around.
You cannot approach it, though, as strictly an experience-building opportunity. The military, even with the Guard, is a career. You should approach it accordingly, with "pilot" being your particular speciality.
Assuming you meet all the military physical quals, you should go for it if you have any chance at all for a slot. Best of luck with your decision.