Criminals go where crime is easier and where they can avoid attention.

For example, I mention that every adult must pay a $30 application fee, pass my credit/criminal background, make a combined income of 3x the rent, and whether or not the property accepts pets.

If you see somone with a high level of recent misdemeanor criminal activity their chances of getting a felony is high.  

Yes, most of the reputable lenders have a min loan amount of 65k - 75k with a minimum of 40k - 50k of that amount going toward the purchase.I've been down this road before with a few investors who want to buy cheaper homes and what I can tell you is that - 1) It's not easy and 2) You WILL NOT like the rates, fees, and points.Think about it, what does a lender stand to make on an interest only loan for about 40k. 

For example, my ad will state whether we accept pets, that we want provide income around 3x the rent, and that every adult must pass a credit/criminal screening.

Worse case, someone gets hurt or killed and you could be held criminally liable as part of the conspiracy to commit the crime even though you didn't intend the result.  

I’ve been down that road, and the constant manual updates get exhausting.

We don't have an instruction manual, crystal ball to the future, or a road map with guaranteed outcomes. 

I'm ready to take the next steps to get the next deal and more further down the road.

So...am I shooting myself in the foot if I buy an investment property now (out of state) to begin my real estate career, and lose out on the ability to use an FHA in LA down the road?