So although the goal is increasing rental income, I would also focus on decreasing expenses.

Either a lender or an agent is going to want to feel confident that you are working with someone on the other side that will actually be able to help you and will get the deal done but as long as the professional you choose has that ability there is no reason that would increase/decrease your relationship with them.In terms of the credit check - this is important. 

In an environment where rates are decreasing you could temporarily get a larger reduction in monthly payments and (hopefully) be able to refinance at a lower, permanent rate sometime in the future.

Taking on deals like this that decrease wealth, such as low return high upfront cost whole life insurance, paying 19% interest on credit card debt, paying 2% annually to have a “wealth advisor” place your money in Vanguard Index Funds, paying for a high cost mortgage because you’re credit is bad, and “debt consolidation” programs are all reasons adding up to why many people can’t achieve financial independence and remain dependent on working every day to live paycheck to paycheck.There is a chance that in a particular circumstance any of these, including the program offer you describe, can be beneficial in certain specific cases.  

On Hawaiian island, the number of visitors to Hawaii from the mainland US decreased by 10% but specific islands like Maui got hit the worst by 30-40% (?).

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) 

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.

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.