Do you have affiliation with any affinity engineering groups (AIChE, NSBE, SWE, ASME)? Their national conferences are typically held in the fall, and the career fairs at these conferences is amazing. I went to the SWE event last year as a recruiter, and we were looking for both new grads and experienced hires. With our company, an early Q1 move from an October-ish conference is not extraordinary. I believe the SWE conference is in Nashville this fall, which is a pretty decent drive for much of the mid-west (spoken by someone who drove 23 hrs home for 6 years at Christmas).
Don't talk about the relocation expenses until an offer is on the table. Plus, it's a question to ask, not a demand. (We completely ruled out a promising person because during her interview, she asked about job placement for her boyfriend. First of all, it's your interview, not his. Second, no ring = no benefits.)