Join Date: May 2000
Location: Houston, TX, USA
Programs: UA 1K, AA Lifetime Platinum, DL Platinum, Honors Diamond, Bonvoy Titanium, Hertz Platinum
Posts: 7,969
Once you have the exchange order, that's all you need and you won't have to pay any more (or get a refund) if the exchange rate has changed since then. If some is willing to sell you an exchange order today at an exchange rate better than the current rate, then they're eating the difference (which makes me suspicious that they'd actually do so - perhaps their website is just out of date).
As you've found out, the Tokyo-Kyoto-Tokyo route is the classic "break-even" route for the JR Pass. You won't be making a big mistake either way.
Also, the Grand Hyatt Tokyo is near the Roppongi subway station, but not within walking distance of any JR station. So, if you want to take the trains to/from your hotel, you'll have to take the subway at least part of the way, and the JR Pass doesn't work on the subway.