I got a quote for roof repair, but of course we are on a time crunch due to the contract, and as always you never know how much more damage they find when they open things up.

Specifically i found that we had to coordinate keys, the seller move out, the closing times, wiring instructions, and various other little details to get the deal done... being this was our first one, it was unclear who communicates all of these as there was obviously no agents or brokers involved.  

I having a hard time pulling comps in the immediate area.

You may have considerable vacancy time.

This is a dumbed down math, but if you PITI is $126 higher but you're getting $16,626 more, it would take a long time until you break even and you'd probably be refinanced by then.

The seller will not let us extend due diligence and will just put it back on the market and said he could do these repairs for half of the cost of the low bid (~5k).

I would say compare terms, seasoning period requirements (Assuming when you mentioned construction loan you're talking about a rehab project), response time of your rep, learn as much about their loan underwriting and approval process as you can.

This timing worked well when one of my rentals had been vacant for a few weeks, and I had trouble finding a good tenant.

For instance, in my market I need to make a hurricane evac plan for my team and inform my guests in a timely fashion to evac. 

But the weren't set to expire until 2020 so I had time.