Update: True to form, "dumpster fire" management (DFM) followed up early last week asking for a timeline on a response. I responded to them last Friday by attaching a proposal from my consulting company with an itemization of the project requirements and deliverables along with the costs.
That was Friday afternoon and they responded by email just after lunch today. Apparently, now it's DFM that's offended by my offer.
Not sure what more there is for me to say to DFM, but I'll probably still wait another day or two before making it clear my offer is, "take it or leave it."
Also, DFM did hire someone to fill that gap, except that person spent the past several years fulfilling the romantic needs of her boss.