Yes, as stated on the page, I wanted to calculate a reasonable upper bound that could not be exceeded.

The lower bound can be estimated easily by not placing the kings on the board at the end, and restricting the pawn count as you indicated. It gets messy though, when you consider a position that has a legal en passant capture, even though not executed, can also look the same as a position where the en passant capture opportunity has expired. These identical board setups are actually two different positions.

The same is true of castling rites. If I move my king to the left, then move it back to the original square, but it looks like I can castle, it is really a different position than an indentical setup wherein I have not moved the king.

If someone wants to work out the numbers to that level of detail, they are welcomed to it!

I also made a formula error for the Bishops. I listed them as a summation of a choose formula, rather than of the form (T/2)^2 where T is the total number of vacant squares that 2 opposite color bishops can occupy. The formula should not be T choose 2 as I indicated at the top of the page, since that implies the Bishops can be both on the same color squares.

I did explain this part of the calculation properly but I did not redraw the formula yet.