it would be great to build even greater equity in our place, in time for our next move
It doesn't really matter whether you build greater equity in your place, money in the bank, ISA, etc so long as you can access it when you buy the next place. It doesn't matter where the money comes from
If you're disciplined enough to save or overpay then the term doesn't mean that much.
If, on the other hand, if you have money you spend money then it may be best forcing yourself to put it into your mortgage by reducing the term and increasing repayments.