First off, THANK YOU all so much for your opinions and insights and suggestions. You helped in some ways you probably know and some you don't even imagine.
M and I talked last night and I now have a little more information about the hiring process. It turns out that because it is a state job, there are 2-3 months full of bureaucratic hurdles to clear before anyone will be hired. 2-3 months! That means they plan to offer the job to someone between June 18th and July 18th, give or take. If we continue with IVF and if everything stays on schedule, our beta will be around June 16th-ish. If we are willing to go ahead with paying out of pocket rather than waiting to see if I might or might not get some infertility coverage, we can most likely have an answer from our IVF cycle before the job offer goes out. So, the current plan (as of noon today - give it a few days, hours or minutes and it may change) is to push ahead with IVF as scheduled and also apply for the new position. Perhaps I'll hear back sometime during our cycle that I'm out of the running for the job, or perhaps I'll get a BFP before a hiring decision is made at which point I'll withdraw my application from consideration. The only way we could find ourselves in a bit of a sticky situation is I'm offered the job and the hiring process takes much less time than they expect it to - like if I'm the only qualified applicant or something (unlikely). If that happens, hopefully it will be close enough to our beta that I can tell them I need a few days before I can give them an answer. If it's too far away from our beta to do that... well, I don't know but we'll just figure it out if and when we have to!