Just like the current, crazy housing market can make people do stupid things like bid over ask, waive inspections, etc., the current crazy employment market can make companies consider crazy things, too.
Do you have any time limit in your decision making? For example, are you putting off something else while you are waiting on the outcome of this? Or do you expect to commit a lot of time to something in the coming months, that this would replace?
If not, then I would expect you have a lot of leverage in the discussion. Because if this truly is project work, and is an approved project, then this likely has a ticking clock already.
Asymmetric pressure is always a great advantage in negotiation. If they deliver it to you in writing on a silver platter, then maybe it's a fun distraction.