While you're very likely right, if the most important thing out of this entire discussion that the OP needs to get is you cannot accept the offer as is. They se

While you're very likely right, if the most important thing out of this entire discussion that the OP needs to get is you cannot accept the offer as is. They seem to actually believe the offerer that they aren't going to make another. Well then, at this point then, they just really need to go 'well that's crap' and toss it in if they're unwilling to counter. They have to get to the point of accepting that accepting it is the absolutely worse thing they could do. Ending negotiations is far far far superior to actually accepting that offer. Once they accept that, then they can counter, confident they're not losing anything. Even if this truly is the last offer, that's a better result than acceptance.