So, back to the original question, what strategies or approaches have BP members used for securing private money lending for a down payment (knowing refinance will produce ability to pull out that down payment in equity in a short amount of time, to pay off private lenders quickly)?

If its 4 units or less the income approach which Cap rates are used not so relevant. residential units are appraised by per unit precises and CMA of comparable sales. 

I’m looking to buy a mobile home park and have started approaching a couple brokers to get info about properties.

How should I approach this or should i just Run for the hills?

The industry term for this is “dealer property” there is a great deal of case law on the issue as to what you should be considering in performing this analysis.If the property is treated as inventory, the gain is ordinary income, not capital gain.A conservative approach is to hold the property 2-years post completion to treat it as a capital asset.You should speak to your tax advisor on this issue as it is a complex analysis.

Interested in learning more about the BRRR approach you guys are speaking on. 

It seems (in my limited experience) that every time one approaches a 'realtor...' they either consider an REI a "competitor?"

Exceptions can be if the location you have is incredible and there is no other site to go on.

Cap Imp vs Repair Expense IRSI'm in the middle of doing some 2017 tax crunching last minute so of course I am on Bigger Pockets forum instead of finishing up my taxes :-)Anyways here's a useful tip on Cap Improvement vs Repair ExpensesMy strategy has always been to increase regular maintenance, repairs (Repair Costs) and spread out costs over time instead of the hands off approach to defer maintenance into larger Capital Improvement expenses. 

I agree that a more personalized approach should yield better results.