Quite a bit of variables that change how much your down payment would influence your mortgage costs which would also lead into your COC and ROI. 

We have coached a lot of our first time home buyers last year to use family funds to make a cash offer and then refi, so the influences the data a little.

Don't let future scenario influenced you too much, because it may not play out.I personally try to avoid any investment that introduces an increasing cost (such as coop fees or HOA fees).

Loan-to-value is a lender criterion that has a significant influence on interest rates and 70% is a safe bet for banker on mortgage.

Are there other factors such as appraisal value that can influence the time line for PMI Requirmemts?

The real estate agent must disclose anything that might influence the buyer's purchase decision - IF - he knows about it.The exception is if the seller fills out the optional "Seller's Statement of Property Condition". 

And influence the path this takes?

Actually, it's not marketing in the conventional way as much as it is networking, having persons in areas of influence or in positions that can facilitate opportunities that feed business to you.Consider building a loan servicing activity in your name.

Kinda like calling the cops for hitting myself and them charging me for assault.This is just thinking out loud.If I went to B of A and had a friend who was able to grant me loans, or influence the granting of loans, and he agreed to commit fraud with me (whether as a favor, carelessness, or for nefarious purpose); don't you think a lender could then sue, "themselves".

My offer is more dependent on my system for crunching numbers and less on what they owe, but if I were to say that what they owe doesn't influence my offer sometimes I would be lying.Now this practice when buying has made/saved me thousands and thousands of dollars, and on the flip side I have lost several deals because I was haggling.