So we are doing deals with cash buyers, no inspection contingencies, and (ahem) pretty low offers.

We got a property inspection which helped us negotiate.

Had to do an HVAC inspection per city inspection (sec 8)  they charged me $350 and the city did not accept their HVAC inspection  so I had to call one myself because of time sensitivity.

Was it found on the inspection? 

Very similar to their Premier Agent system.Zillow's instant offer is verified by a real estate agent who meets the seller and walks the property to verify condition (Zillow also does inspections to drop their price further if Seller accepts it) but the agent's goal is to take a listing by showing the seller how much more money they'd net, NOT to talk them into taking Zillow's offer.

I issued a draw to our HVAC/Plumbing contractor to get this project to the rough-in inspection. 

@Jonathan Barr it might be worth looking into properties where the inspection reports are provided upfront.

I would take the opportunity to ask them if there is any other maintenance issues, go over there, and do a full inspection.

Should we ask to skip inspection since they have been living in the house for 6 years?

If they are moving out, you do an inspection AFTER they have moved out documenting anything that is not normal wear and tear (take photos).