Look into STEM OPT extension. It's good for 17 months. Your student advisor should know about it and your employer must be enrolled in E-Verify. You'll need the employers E-Verify # when applying and you'll get a new I-20 from your school. Nothing with USCIS is ever that simple but the employers I work with have lots of F-1 students that qualify and quite easily get their STEM OPT extension. You have to apply well before your OPT expires though (90-120 days).
Yeah, we thought about the OPT extension. The problem is that we're not enrolled in e-verify, and the company that we outsource HR etc. too doesn't do it at the moment either.
We might go down that path anyways if H1B fails; we'll see what happens.
Enrolling in E-Verify is very easy and if the company you outsource HR to can't process E-Verify for your I-9 Forms I'd be extremely worried.
A backup plan I've been thinking about would be to move to the Canadian west coast if I don't get a visa (EU citizens, your country may or may not have visa agreements with Canada that allow you to work there- France has nice things in that regard) to be not too far from my team.