Had a nice positive cashflow until approximately 1 year ago when I had increase in property tax and HOA, plus had  insurance increase, which decreased my cash flow to nearly $0.

I would qualify it with in today’s seemingly rate decreasing environment, I might look to trying to recoup costs in 12-18 months (or less) 

Those two things will result in higher payments and decrease cash flow.

Now, property values have dropped—almost to the point where the capital gain tax I avoided through the exchange is offset by the decreased value.Has anyone found an effective 1031 exchange strategy that allows you to take advantage of the tax benefits while still buying the replacement property at a good price?"

If you're switching from STR, you should expect a decrease in ROI since MTRs earn less than STRs in general.

(I have five rentals).Thanks What Russell said, you can decrease that liability as much as possible on making sure you line out the 593 form. 

A few weeks ago we decreased the list prince by 5%. 

Avoid anything with condo association fees or homeowner association fees as they DECREASE CASH FLOW with no real contribution to the bottom line.Lastly, since you are new, when you do get a property DO NOT HIRE A PROPERTY MANAGER.  

I think the main drawback is being on a Prepayment Penalty in a rate decreasing environment.

It is rare that investing money in a property would DECREASE the value, but will this investment increase the value of your property?