The main issue is a consistent lack of effective management and oversight.

There's some mis-information and mis-understanding of AP, the process and it's effect in this thread.

What considerations would be required to address before making a “Yay or Nay” decision to move on an out of state multifamily property.Toughts anyone? 

If you have not heard of the Dunning Kruger effect, look it up.

For instance, one investor I worked with used it to jump from a duplex to a 4-unit building in Phoenix, effectively doubling their rental income as well as the forecasted appreciation rate on their new property.

Buying an out of state rental property from a realtor, wholesaler or off facebook or zillow etc as opposed to from an operation or turnkey provider who has an active, substancial, and effective boots on the ground team or teams to support you after you close on the sale. 

I have an applicant who says she lived in the Dominican Republic prior to the 2 years she's been at her current address.

.- there are ways to never pay tax on gains (1031, owe until death, etc)- cost segregation can in effect have RE acquired at no cost- sweat equity can produce additional return.  

Which would be more effective for pitching my Airbnb arbitrage business?

Kudos to you all for taking the time to address the main considerations (timelines, finances, relationships/family planning, etc) before getting too far down the path.