@Joshua S. You may not have gotten a mortgage larger than was necessary, but your previous example did.
As to where the lost money went in your lottery situation, lets run the full numbers step-by-step...If we do the math correctly, there will be no mystery money involved, and every verification will arrive at the same answer.
The month has rolled, so the numbers may be slightly different than you just noted based on keeping the pay down of $130k in Jan 2023, but the math is all the same. As a reminder for any future reference, we're using the calculator on a $165k, 30 year, 4.5% mortgage.
1) Baseline math. Full 30 year mortgage = 135,971.07 interest. With $130k paydown in Jan 2023 = 30,662.20 interest. Total interest saved = 105,308.87.
2) All payments up to Jan 2023 can be ignored, because they were on schedule regardless of how we change things at that date. So we basically have a 153,596.27 loan on a 312 month term. This results in the same exact $836.03 monthly payment, and more importantly is how the interest math adds up. Full 312 month = 107,245.32 interest. With 1st month $130k paydown = 1,936.45 interest and payoff would be in a mere 31 months. Total interest saved = 105,308.87. Comparing back to (1), so far so good.
3) At this point, it's exactly what I was talking about with your last example. After the $130k paydown, you are basically running a 23,336.23 loan on a 312 month term. Full 312 month interest would be $16,475.59. Remember this number for later. As it stands, this would have had a $127.02 monthly payment. However, because your mortgage was set up with an 836.03 monthly payment, you're effectively forcing a 709.01 monthly over-payment. The result is paying it off in only 30 months with interest = 1360.47.
4) But wait, the pay off was in 31 months before. Where did that extra month go? That's the month that had interest charged on the full $153,596.27 balance. This 1 month = 575.99 interest.
5) So what happens when we add the 30 months of interest from (3) to the 1 month interest from (4)? We get 1936.46 in 31 months of interest...Exactly the same, well within a 0.01 rounding error, of the interest from (2). Again, since the math checks out, so far so good.
6) Remember that 16,475.59 interest that would have been paid over the full 312 month term in (3), by subtracting out the 1936.46 31 month pay off interest, there is a 14,539.13 interest savings from the forced 'over-payments'.
7) Starting with the verified total of 105,308.87 in total interest savings, and subtracting out the 14,539.13 in 'over-payment' interest savings, that leaves us with 90,769.74 of remaining 'unaccounted for' interest savings.
8) Now if we plug a $130 'loan' in at a 312 month term, we get...90,769.73 in interest that would have been charged. Oh hey, within 0.01 again. Looks like that is the amount of interest savings that can be directly attributed to the $130k pay-down itself.
9) For fun, lets try one last mathematical 'verification'. Plug in a $10k loan @ 312 months. Total interest is 6,982.29. Now multiply that by 13, to get a $130k equivalent, and it's 90,769.77. A few pennies extra off due to rounding over the life of each lower value loan compounding with the number of 'micro-loans' needed to get to the same total...And one more time with a $1k loan @312 months. Total interest is 698.23. Multiplied by 130, to get a $130k equivalent, and it's 90,769.90.
No matter how you slice it, the math ALL agrees. Quite simply, the amount of interest saved that can be directly attributed to any given amount of early pay-down, is the same value as the interest which would have been paid on a hypothetical loan for that early pay-down amount over a term the same as the remaining on the mortgage at the time of the early pay-down. No more. No less. The remaining interest savings is inherently coming from what are nothing more than over-payments 'hidden' within the remainder of your standard monthly mortgage payment. Thought of another way, these over-payments could be eliminated by refinancing with with the same term on the refi as was remaining on the mortgage before the extra pay-down, assuming there was no additional cost to do so.