@Roy N.
You're absolutely right. I did the math...
Loan Details
200K
30 years
4% interest
Starts on March 1, 2019
With Nothing Extra
Last Payment = (2/1/2049) 360 months
Total Interest = $143,739.02
Strategy A: Extra Principal = 1K per Month
Last Payment = (8/1/2029) 125 months
Total Interest = $45,007.70
Strategy B: Extra Principal = 12K per Year
Last Payment = (3/1/2029) 120 months
Total Interest = $42,213.1
The idea of using a simple line of credit (HELOC, credit card, or whatever) to make large payments on the the principal of your amortized loan in an effort to reduce the total interest that accumulates does work. However, its not significantly better than just making extra principal payments.
With both strategies illustrated above you are committing to making an extra 1K payment per month. Strategy A pays that directly to the principal on the mortgage and strategy B pays it to the line of credit that was used to make an annual payment of equal value to the principal of the mortgage (to pay earlier). Of course, there will be a fee for using the line of credit, which will vary depending on the terms, but will most likely put strategy B behind overall.
With that said, strategy B does have a benefit that strategy A does not. Strategy B will likely improve your credit score and cause banks and other lenders to increase your credit limits.
I crunched the numbers using this calculator (no affiliation)... http://mortgage-x.com/calculators/extra_payment_ca..