The house that sadists built: Selling

So a little over a week ago, we got the surprising news that an offer was being made on the house.  (Hallelujah chorus begins)

Said offer was 8.9k less than our listed price.
(Awwss... chorus still plays, but more quietly)

However it is a cash offer with only the standard home inspection contingeny.
(Resume chorus at full strength)

We take the offer (with a quickness) and only ask for a slightly more realistic settlement date so we have time to move out.
(dancing!)

The buyer agrees and arranges for an inspection the next day.  Turns out, he's an investor with staff.  We don't care - we're free!
(Holy Ghost Dancing? Why yes, thank you!)

After the inspection, the buyer is "surprised" to "discover" that we don't have AC in the almost 40 year old house.  Something clearly stated in our listing, by the realtors, and in the contract THE BUYER drew up and sent to us when he made the offer.
(Record rips to a stop.   Foot tapping commences)

We suspect he's trying to get a lower price.  We go back and forth for days, but ultimately it's still a competitive bid and it's cash.  We begrudgingly accept his new counteroffer but are informed that was a verbal offer (still legal in VA) but we haven't seen a signed contract.  I am starting to smell something rotten.

It's this house!

However, we still have tiny spurts of hope that this will still turn out to be a solid sale.  We were so closed to being free...