Following the play book on something like this can be worked through.  

Then you also have the curb and curb size as well as traffic count that all could come in to play.

I'll have to be more conservative in the rehab projects I take on until I'm better at estimating and I have more free cash to play with. 

If extending it is the right play for you (risk wise) then I would find a way to sweeten the deal for the sellers, otherwise where is their incentive to play nice and let god knows what happen to the property in the next several months knowing its vacant.

I can see 2 ways this plays out: 1) RE falls significantly 2) RE holds its current value. 

Another possibility, would the seller consider pushing closing back a couple of months to see how this all plays out?

All of a sudden your deal is null and void(probably wouldnt hold up in court anyway-tenant can say was under intense  duress).   

And it seems to me, that if you can be liquid whether with experience or not, that the playing field will be shrinking here soon.

We will know soon enough if they will continue to pay rent or play games. 

IMO, he's just playing you to see if his can skip the application steps & don't need to provide unfavorable information (if he has trouble filling out an online application, he will also have trouble holding a job & have trouble paying rent).