First, the main benefit of a larger down payment is avoiding private mortgage insurance (PMI).
The effect on the interest rate is generally small, if you have good credit and are putting at least 5% down (less than 95% loan-to-value). See here for an idea of how federal mortgage agencies price the effect on loan risk (which passes through to your interest rate).
Apart from PMI and interest rate, increasing the down payment obviously reduces the loan amount for a given house, reducing the total interest you will pay. It is similar to paying down any other loan, so you would prioritize loans with the highest rate (or keep the money invested if you can earn an even higher rate).
EDIT: I agree there are some bumps in the LLPA table that seem anomalous. My main point is that the down payment effect on risk pricing is quite small and can probably be neglected in your modeling. According to the linked article, the percentage in the table is a one-time charge on the loan amount (but incorporated into your loan costs, not owed by you up front). Thus, roughly, you'd divide it by something like the number of years in the mortgage to get an effective interest rate delta.
Most important in choosing the down payment is to put enough down to avoid PMI if you can, and to compare your likely mortgage interest rate with other loans and investments. The nice thing is that mortgages generally have no prepayment penalty, so if you end up wishing you had put more down to reduce the loan balance, you can make one or more larger payments and get a similar total-interest-saving effect.