I've purchased a couple of my investment properties directly from property management clients who decided to sell. 

You could trim your expenses by eliminating property management - you can absolutely do this yourself on a 6-unit, even as a newbie.

Has anyone come across their property management company creating a "First right of refusal program" for maintenance requests? 

I would also add, a contractor that you can buy materials for and they know how to put them in with little to know direction (reduces the management time of the project).

Self managing should be easy, if not then that Realtor can probably help you with the rental side of it. 

Self-Employment Opportunities: Would it make sense to start a side business related to my rental properties (such as property management) to access more deductions?

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I've managed a number of successful rehabs and put a lot of sweat into them as well.

I recommend that they use a property manager.

Hey Jamie, I am actually a property manager located in Jacksonville, FL and work with several investors in the area.