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.  

Last year, they ceased syndication with Zillow for marketing and it's killing me. 

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.

For this post, I am trying to find out more about the real estate market local to me.

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

The American market isn't strictly RE driven. 

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

SF houses are easier to maintain, have greater appreciation rates, and appeal to a bigger buyer market.

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.

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