So then the house is 10% owned by The Person, and 90% owned by The LLC (income and expenses shared accordingly).Now this year say I want to take the same percentage (10%) - and say it's a flat market and the house is still appraised at $500,000.  

Really important to do the market research, check for liens, and get eyes on it before waving that paddle at an auction. 

This might mean refinancing or using a HELOC (Home Equity Line of Credit) to access capital for your next investment.

The American market isn't strictly RE driven. 

We spent four years in a duplex, maintaining it in our rental portfolio as we transitioned to another house hack residence with an additional accessory dwelling unit-type house next door.Navigating the intricacies of FHA loans in competitive real estate markets can be daunting, given stringent home requirements and more complex processes.

In the Phoenix, AZ market Ceiling Fans are very popular and definitely increase the desirability of a property.

I suggest talking with @Connor Gillen who has a strong grasp of the market up there

You cannot use "short term rental income" to qualify on the subject property BUT you can use 75% of the appraiser's rent valuation on the 1007 market rent schedule.

The value adds and the market appreciation profits pale the cash flow (this is even with a duplex that cash flows over $5K/month).

Evening from Alaska, My business partner and I are new to real estate investing and trying to get our first deal going in a high-interest rate market.