I assume you would either give them a discount on their rent or free rent for their service as a result. 

I've got at 2.29% rate on the current primary and a mortgage payment all in of about $2600.

You should probably place more equity in this deal and refi once rates drop or sell it if you can't take the cashflow losses.

Obviously, you don't want to have a high interest rate locked in, but if it is the only way to close on an otherwise good deal, the short term cost may be worth it.

It's worth considering the credit rating of an insurance company and how long they've been in business. 

Three years ago, my wife and I purchased a duplex with a 3.25% interest rate.

We are looking for properties in a B or C area with a B or C rating and most importantly, the investment property should have a value-add capability.Ideally, we are looking at properties between 50 and 200 units but if close enough and a win-win, we will to take a look.Contact me if you are a serious seller or Seller Broker/Agent.

They will often sell a loan at a discount if it's really bad.

This is because FHA loans are assumable, which means that a potential buyer is willing to pay a higher price for a home if they can take over the existing low-interest rate mortgage.

You may also be able to get a group discount if you do multiple individual loans (although I cannot speak for every lender on this).