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@Dammit
We did a variation on this theme - kept the term as it was, dropped the interest rate significantly, then kept the payment the same, effectively over-paying every month.
The advantage of this is that the overpayment gets taken off the capital, whilst the standard payment goes toward the interest (mainly, at first), and it drops the term exactly as in Souls example but without being committed to it, so we could change the repayment amount to the actual figure if we needed to at some point (as unlikely as that is).