Okie doke, Sunday morning and time to think. Let me get the core concepts understood:
1) We're looking for an inaccurate number of failed cycles. If we adjust a total on the portfolio with some change in the calculation, but that adjusted total is not sufficient to change the number of failed cycles, then it is nitpicking even if the portfolio value changes what appears to be a significant amount. Nothing is significant and wastes your time unless it changes the number of failed cycles. I think this is clearly true. The number of failed cycles is what determines confidence level so that is all that matters.
2) Apparently your implementation of inflation on spending is done in January, but uses December's inflation measure (??). This means that for year 1876, you apply the (Dec) end of year inflation measurement to the year's spending -- even though you're going to pre-spend that money in January. And because you prespend that money in January, that year's spending does not reside for any months in an interest bearing account and does not grow.
3) I said 1876 in item 2) but you also do the same thing in year 0 (1871?). 1871's end-of-year reported inflation determines the spending level of 1871, after being added to the user's input number for first year spending. So if a user says his first year's spending will be 30,000, you will actually spend in that first year (30000 X (1.0 + infl rate)).
Okay jdw_fire pointed out that if we presume that short term rates are pretty close historically to inflation, anything done to say that spending is spread over the year means that inflation cancels growth. I think this is true. The only question is does "inflation cancels growth" constitute an increase or decrease in portfolio size in comparison to the current algorithm (and of course if that size change is big enough to generate new cycle survivals/failures).
dory, your post seemed to try to explore any difference in inflation vs short term returns as the year traverses and yeah, that's pretty convincing that such an amount will be small (though it will compound as an annuity, with year 0 compounded 30 yrs, year 1 compounded 29 yrs etc), but I suspect it is not going to generate a cycle survival/failure change so that is persuasive.
The only remaining doubt I would suggest is that a user specifies a first year spending value and that is not what he or she gets. He gets the number he or she specified plus that year's inflation. This difference is not going to compound (I don't think), but it means one year's worth of inflation will affect the successful SWR. I'm guessing small potatos and at most this might change one cycle, but I'm not sure.
Anyway, thanks for entertaining the questions.