Just curious, What is the loan amount (and LTV) we are looking at, and how far is the 2nd home from the 1st home (your original owner occupied home) ?
You want to convert your primary home to a rental property and buy a new home as your primary home.
If one lender objects to this, your loan broker should find another lender who would loan you on new purchase as primary home.
I think your explanation letter looks reasonable. In the worst case, if you are forced to purchase the 2nd home as rental, keep it for 6-12 months and refi again as owner occupied property.
The rate between owner occupied and Rental may defer anywhere from 1/2 percent to 1 percent.
So, if you like your new home and you like the price, you might have to take this hit. For every 100000 loan amount that hit could be about $300 of extra payment till the time you can refi with owner occupied rate.
But, personally, I am not seeing much issue in your case. Your loan broker just has to find someone who will be willing to lend.