Ok, I think I understand the terms now. However, I don't know how to make it work so that the "return" on the lump sum is the same as the mortgage rate. Here's the decreasing mortgage balance for the 100k and 90k principals in the OP's example:

At all times

, the difference between the balances outstanding (i.e. the height of the blue strip) is equal to

. That is, we seem to be saving an amount equal to the value of the lump sum compounded at the mortgage interest rate. But then the blue strip between

and

includes an additional interest component that I have not accounted for. If I include this I don't get the mortgage interest rate whether I spread the savings over

or

periods (it's higher or lower than the mortgage rate, respectively). I presume this is where your "reducing balance" comes in, but I don't know what balance you are talking about or how to factor it in.