I serve on committees when able, and generally be understanding that a program aligned with our federal HUD is going to have it's inefficiencies.

An LLC doesn't make a difference in your federal taxes or what you can deduct.What you want to do is technically possible, but there are several hurdles. 

The interest on the rental is an offset to rental income, and is by definition deducted from your taxes.A 4% interest rate on a primary is like a 4.88% after rate for a taxpayer in the 22% federal tax bracket, or higher if in a state with state income taxes. 

Within the first month I believe the company byte federal has a data breach.

Another downside is you loose on the advantages, of the Federal Tax Code, by not closing in the name of a LLC (you can elect to have a LLC taxed, as a S Corporation which is a whole other conversation).If you want to close in the name of a LLC, Mortgage Lenders will offer you Commercial Loan Terms (25-30% down, a 15-25 year amortization, and a ballon due in 5-7 years).

Maybe not anymore, for now: https://natlawreview.com/article/texas-federal-court-issues-nationwide-injunction-against-enforcement-corporate

(As AZ and your current state will fight over who gets to tax your gains with the federal government.)I have to throw most of the shade on your horrible tax guy/cpa who didn’t tell you renting it out was a $50-$100k mistake. 

Many borrowers file this form as an exclusion to their US federal taxes as they may have been taxed by the country where they are earning the income.Required Documentation for Foreign IncomeWhen it comes to processing foreign income for a loan, documents required may include:» Most recent personal tax returns» History of receipt» Proof of continuance of foreign income earnings» Conversion of the income from the foreign currency to US dollarsThese documents must be translated or completed in English so that a loan reviewer can properly evaluate the information provided.Fannie Mae & Freddie Mac GuidelinesIncome from Foreign SourceIncome from foreign sources must be reported on the borrower’s most recent U.S. individual federal income tax returns.

Show them the history of 30 year fixed mortgage rate & explain that the only reason rates got as low as they did is because the Federal Reserve started Quantitative Easing during the during the recession and then again during COVID.Here's the graph showing the impact of Quantitative Easing (QE) on interest rates.

https://natlawreview.com/article/texas-federal-court-issues-nationwide-injunction-against-enforcement-corporate“We note this is a preliminary injunction, and we urge reporting companies to pay attention for additional updates and proceedings in this and other cases which could modify or change this order.”