The objection comes up in the first ten minutes of every conversation, and it's the right objection. Your mortgage is at 3.5%. The line of credit is at 8.5%. Moving money from the cheap debt to the expensive one looks like it has to lose.
It sometimes does. The reason it sometimes doesn't is that the two loans charge interest on completely different balances. The mortgage charges its rate on $340,000 for thirty years. The line of credit charges its rate on an average daily balance that starts at $15,000 and falls every time a paycheck lands. Rate times balance times time is the whole calculation, and the balance term is doing more work than the rate term.
Run it. A $15,000 chunk against a 3.5% mortgage with 26 years left kills roughly $20,000 of future interest at that rate and term. Carrying $15,000 on an 8.5% line of credit for fourteen months, with the balance dropping steadily as income sweeps through, costs somewhere around $700 to $800. Those aren't close.
Where it flips: a very short remaining mortgage term. Nine years left means the interest a chunk would kill is small, because most of the remaining payments are principal already. Chunking into the tail end of a mortgage is close to a wash and sometimes a loss. That's the case where paying extra out of cash flow, without borrowing, is the better answer.
It also flips if the payback stretches. The comparison above assumes fourteen months. Stretch it to four years because the surplus was overstated, and the line of credit interest climbs while the mortgage savings stay fixed. The rate spread matters more the longer you carry it, which is another way of saying the rate spread is really a warning about slow paybacks.
The rate on the line of credit is also variable, and 8.5% today can be 10.5% in eighteen months. Stress test at three points above where you are. If the plan only works at today's rate, it isn't a plan.
One structural note. If your mortgage is at 3.5%, you have a cheap thirty-year loan nobody is going to hand you again soon. Some households look at that and decide the right move is to leave the mortgage alone and point the line of credit at other things entirely. That's a defensible call, and it turns on what else you'd do with the money.