We have done well investing in 0-5% in personal homes and than saving the rest of the down payment for the 20-25% pure investments.

We used the profit from the house and our savings to than supplement that with pure rentals to grow our houses quicker.

Are there factors within my control or specific to my situation that influence this, or is it purely based on lender policy?

Weather or not you put 20% down to avoid PMI is purely a math personal decision that you have to make. there will be some folks that tell you 20% down is better and others that tell you go as low as you can.  

From a pure financial standpoint, assuming all houses cash flow well, it is better to have 5 houses than one.

This post is purely for ***** and giggles to break up the monotony before I burn out.

Not in town enough.Are you purely in residential?  

FHA loans are pure brain damage. 

If pure appreciation is your investment goal, than Kansas City would not be a good market for you.  

The rainy day fund is already a set aside amount of cash that I suppose could be invested in short terms (again boring) CDs or purely safe vehicles.