Or might it be better to wait it out and accumulate as much capital as possible?  

Anything above that could start significantly (and permanently) impacting your monthly net (reducing your returns), and will accumulate quickly if you plan to keep the property for a long time. 

And pay off any consumer debt you've accumulated (credit card, student loans).

What are you goals, first: Is it to accumulate large sums of cash, is it to have steady flowing income each month.

You new accumulative CF is now 8400 + 3600 + 5000 = 17k/yr.4 - Now take 2 years of CF (17k/ea yr) and use that as a 20% DP (34k)and you have an added property worth 170k.5 - If that property CF at 7k/yr, your new CF would be 24k/yr.6 - Now take one year of CF (24k) and buy a 120k property with CF at 5k. 

Since that time I've been blessed to have accumulated a lot of cash on hand, and am interested in refinancing those properties using my own private money.  

The issue is probably not the house next door, it is most likely lack of proper drainage around your house so the water accumulates/sits around your property instead of flowing away and lack of proper waterproofing to the exterior of the foundation to protect it from water damages 

Although, I do find that ROI takes a small hit, as monthly rates are lower than the accumulative shorter stays.

This is sizable but realistic chunk of cash, that many in our 30's and 40's have already accumulated, either by working for it or through inheritance.

It is a daunting venture for a newbie so I'm taking my time and accumulating existing rentals in the interim.