Asking for a FT Job

Long-time lurker. I am a non-target senior who managed to SA at small shop for traditional "junior" year internship; long story short the shop is no longer around and I feel the rug pulled from under me. Fortunately, before settling for the small shop, I managed to network a BUNCH and got to meet a lot of people at a bunch of different banks/groups. I got offered a F500 corporate finance job and may have to settle for that, but as of now I am on the hunt for a FT IB Analyst or any capital markets job after I graduate in May. 

Does anybody have any suggestions for how I can eloquently re-connect with people I networked with last year and ask them (straight up) for the scoop on full-time recruiting? Some of the places I networked with are really small advisory groups and have less traditional analyst programs, but sometimes advertise on the job sites. How do I go about this? They don't have full on HR teams and I don't wanna come off too forward.