Thanks for the thoughtful comments/suggestions. The thread on not paying off the mortgage was about a primary residence. The assessment for a rental property changes the calculus, as you note. I came to a similar evaluation but looked at the $16.8K in additional annual income slightly differently. I agree that the $260K could be used for a higher-return investment in additional real estate, but we decided that one rental house was all we wanted in the asset mix.
If my $260K in cash is invested rather than paying off the rental mortgage at 3.8%, and we get an average return of 5.8% for 22 years of the remaining loan, we get a net increase of 2% per year more than the mortgage loan. Over the 22 years remaining on the mortgage, we get around $140K in returns above the cost of the mortgage loan. The total cost of the rental property (principal and interest) would be around $560K.
If I pay off the rental mortgage, I get an additional $1,400 monthly or $16,800 yearly, as you noted in positive cash flow. This rental's total positive cash flow is $2,400 per month/$28,800 annually. Over 22 years, assuming the extra $16.8K a year is invested and reinvested with a 5.8% average annual return, we would have around $710K. The total cost of the rental property (principal and interest) would be around $406K.
So, paying off the mortgage now allows me to invest an additional $1.4K a month/$16,800 a year, getting around $570K more compared to maintaining the current mortgage and keeping the $260K invested, and reduces the total cost of the house by $154K, seems attractive.
The initial $260K cash stockpile used to pay off the mortgage is replenished in year 12 if gains from the $16.8K annual investment are reinvested.
Because the fiscal benefits seem strongly in favor of paying off the mortgage, my assumptions must be missing something. I appreciate everyone's thoughts and suggestions.