Inspector keeps insisting that there's something wrong with the HVAC.

I would insist on him puling the permits.

All the more reason to hire a good property manager, or if one insists on self-management, make sure you get to the property at least once a year.

Any potential buyer with an IQ above 50 will insist that these are replaced or they are given a credit. 

But a couple times a year, there is a contractor that the homeowner just insists on using, against our advice. 

It just might be a bit of a needle in a haystack, and you might end up with a less than ideal property if you insist on going that route.

Your lending attorney will know.Last, even though you seem to have enough to make a relatively safe 1st position loan, if you insist on making a 2nd (???)

I offer to send them the amendment myself but they insist it needs to go through their agent.

Here’s what you should do:Pause the closing and request a detailed explanation of the fees and LTV change.Negotiate see if they’ll reduce fees or revert to the original LTV.Explore other lenders who might offer better terms and transparency.Always insist on written terms upfront to avoid surprises.

Yep^^^ It would be like ordering a car to be built, but insisting on providing your own wiring, radio, tires, headliner, etc.....