"Too much Illinois exposure" can mean either thing you named, and there is a real way to tell them apart.
If the issue is the state, a buyer who already owns Illinois assets is genuinely limited. Lenders, partners, and fund mandates often cap concentration by geography. A buyer who put $2.1 million to work in Illinois this quarter may literally be at a ceiling their capital source set. That is a structural no, and lowering your assignment fee would not move them.
If the issue is price dressed up as geography, the tell is what happens when you bring a different buyer from outside Illinois. If that buyer also passes, or passes at the same fee, the deal structure is the problem. If an out-of-state buyer bites, your first buyer was telling the truth about exposure.
So the diagnostic step is simple: put the deal in front of two or three buyers who have no Illinois holdings and see what they say about the numbers. An 8.3 cap with 11% rent upside rolling in 14 months is a story a lot of multifamily buyers will read carefully. Whether they like Peoria specifically is a separate question from whether they like Illinois as a category.
The one thing you may not have asked about: 31 days is tight for commercial assignment. Commercial end buyers typically need time to do their own income underwriting, review leases, and arrange financing or partnership capital. If your contract does not already include a feasibility or inspection period that the buyer can work within, that clock is the real pressure point. I would confirm exactly what your contract allows before you spend days on outreach and then run out of room.
What does your current buyer pool look like outside of Illinois-based operators?