We request an inspection contingent deposit but the seller insisted an as-is offer.  

If they have not seen the property, and insist on an inspection, I anticipate the buyer is just wasting our time.

I have asked him to do his own pest control, but if he insists on my calling the pros again, I'll probably have to cave. 

I don't insist because then I have to police it and I don't want to do that.

Did you still insist on written notice of her intent to vacate?

I told him no i can't pay for it. but he is insisting that i do it and is threatening to move. what's the best way of dealing with it?

But, it's your job to insist :-)

The guy on the phone either pretended to or actually had no idea what I was taking about but after I insisted it be fixed, he transferred me to Customer Retention.

Then the relationship is soured.You may be thinking that your situation is different, but that's what everyone thought before it went bad.If you do insist on doing this, the way to structure the lease, as mentioned above, is to charge her full rent in the lease. 

The upshot is that they don't resort to calling him directly, we still insist on written repair requests, payments through our web portal, etc. and without fail the landlord prefers this.