Super Hakuto fee with Green Car JR Pass

I plan to do a day trip to Tottori from Osaka, combined with a stop at Himeji Castle in the morning. I will have a Green Car JR Pass and will be taking the Super Hakuto train, which I know requires a supplement fee for the non-JR portion of the line. I have a couple of questions about this. One, will boarding at Himeji as opposed to Shin-Osaka affect this fee? (Probably not, since the non-JR section does not start between Osaka and Himeji.) And two, will reserving a Green Car seat affect this fee as well?

One, will boarding at Himeji as opposed to Shin-Osaka affect this fee? (Probably not, since the non-JR section does not start between Osaka and Himeji.)

You correctly answered your own question.

And two, will reserving a Green Car seat affect this fee as well?

The additional fee structure is as follows:
- base fare: +1300 yen
- limited express fare without seat reservation: +420 yen
- limited express fare with seat reservation: +520 yen
- green car supplement: +520 yen

So, if you travel by green car, the total supplement should be 2340 yen if my understanding is correct.

If you use a Green seat, you have to pay the Green fee of the section not covered by your pass.

You correctly answered your own question.

Yeah, I ended up doing that to myself for some of the other questions I wanted to ask. And after reading your answer about the supplement fees, I could have answered that myself as well. I confirmed them by measuring the price of just the Chizu Ezpress track (Kamigori-Chizu). Thank you anyway, it's still good to know!