shopping mortgages when closing costs are covered

Rule #1 - Screw your realtor. This is about you. Not them. They're trying to feed a profit partner for later down the road or get a kickback/bird dog fee.

Rule #2 - Ask each broker to put in writing what PAR pricing is on your loan package is.

IE-For a purchase where you're borrowing 90% of the home's value, with a 760 credit score in an owner occupied single family new construction, what is the rate where the lender makes no money on said interest rate.

That rate based on your specific criteria is considered PAR. The lender cannot sell you a PAR rate or they'd go out of business but you can buy it down.

Rule #3 - Ask them how much it costs to buy your rate down to Par. Then just have your company pay that as part of the closing costs for your loan.

I'm sleepy and leaving some parts of this stream of consciousness out but this will put you in a good decision or position no matter who you choose.