My advice, based on that market, is pull as much equity as you can out of the property and buy as many more as you can afford.

My question is this: Do I need to have my property rented at the increased rent for a full 12 months before I try and refinance to pull cash out?

Reading through some of the posts on the subject in the other threads, I have seen some people state that you can pull off stick built homes for the same cost of construction, but with the current inventory of containers, I am having a very hard time seeing how that is.  

I wish I could just pay a small fee even if it is monthly to see MLS listing.

Is there a standard lease fee ?

Then, I subtract my fee, which has been $5K every time, because anything more, in most cases, would be completely ridiculous from the seller's perspective (as if a 50% of market value offer wasn't ridiculous enough to them already), and anything less would make it hard to recoup my marketing dollars spent.  

I am also looking for an AZ lic RE agent who would be willing to pull comps and help me locate individuals that would advise me on the condition of the homes that I have under contract but no idea of their condition and repo assessments.

That could limit how fast you could refi, pull out the equity and buy the next home.

You have to find out the costs associated with evicting a tenant in your area (lawyer fees, court fees, etc.).  

Do the realtors take a fee for the contract?