A balance falls by whatever is left of your payment after the interest is added. That is the whole mechanism, and it explains why progress feels slow at the start: on a high-rate balance, the interest can take most of a minimum payment, so only a small part reduces what you owe.
The monthly interest is the balance multiplied by the annual rate divided by twelve. If the payment is smaller than that figure, the balance grows even while you pay every month. This is the situation to fix before anything else, and the Debt Payoff Calculator reports it explicitly rather than showing a payoff date that cannot happen.
Once the payment clears the interest, the effect of increasing it is not linear. Adding a small amount every month removes months from the end of the schedule and cuts the total interest disproportionately, because the extra money reduces the balance that future interest is charged on. That is the same compounding mechanism that works in your favour in a savings account, running the other way.
The order in which you attack several debts matters less than most advice suggests. Paying the highest rate first costs the least in total interest; paying the smallest balance first produces earlier wins and is easier to keep up. Both are far better than spreading the spare money evenly and finishing nothing early.
Before consolidating anything, compare the real cost. A new loan only helps if its rate is genuinely lower after fees, and if the old balances are closed rather than left available. The Loan Calculator shows the total repaid rather than the monthly payment, which is the number that makes two offers comparable.