Yeah, my guess is that JL F JFK-NRT is your best bet under the circumstances, followed by other JF F options if that routing proves unavailable. And I'm sure it will be very fine!

In a related time-saving and miles-saving mode if those are priorities, and as a fallback, you could also consider AA (!!!) in F from the USA to NRT, if it offers the 777W with the new F seats on a given route. It won't be the same cultural experience and the service likely won't be as good, but it will get you there with a nice hard product. But based on my own brief inquiries and the post above, I'd think you'll be able to snare two JL F seats.

A few more thoughts:

1. In exploring award space, see if HND (Haneeda) is available. I've never been through there, but it's the "other" Tokyo airport and is actually much closer to town. Some major carriers have started flying there in recent years.
2. Yet another variation on the theme re award space is to see if you could fly into or out of other major Japanese airports such as Nagoya (??) and Osaka for your trip, since they might be closer to where you'll start or end up in Japan. In planning our own wonderful trip, for example, I hadn't focused on the fact that Kyoto is much closer to Osaka than Tokyo, so wasted some time traveling back to Tokyo when flying out of the country.
3. Have you yet gotten and used the Hyatt Visa card that offers two free nights at any Hyatt in the world if space is available (which it generally is, if you book sufficiently far in advance)? Between you and your spouse, you could have four free nights at the Park Hyatt Tokyo, which would save you the conversion of some Chase Ultimate Reward points (which could in turn help open up the possibility of those SQ 380 F suites).
4. The PHT really is a unique hotel and memorable experience, by the way. As you may know, it's not as well situated as the Grand Hyatt, but getting around Tokyo is manageable from there anyway and we're glad we stayed at the PHT. Plus it is perhaps a 20 minute walk from a very nice large park (sorry I can't recall the name, but a map or the PHT can direct you there) that shares some green space with a a large temple area. And roughly on the other side of the park from where the PHT is, there is a major shopping street (that I believe is well known enough that the PHT will know about it) that becomes much more interesting once you branch off of it to the smaller side streets nearby, which have smaller shops, cafes, etc.
5. I've read great reports about the Hyatt Kyoto, so wouldn't discourage you from going there. But if you're looking to save Chase UR points/Hyatt points and if you have some SPG points to burn, one alternative to consider is the Westin Kyoto. It is a big, somewhat westernized hotel that lacks the charm and sophistication that I'd imagine the Hyatt and other properties have. But we found it to be fine (it helped that we lucked out with a rare suite upgrade due to my SPG Platinum status, though we would have liked it anyway) and really liked it's location: walking distance to what we considered the best and prettiest part of Kyoto, the Philosopher's Path that offers an easy stroll through nearby hills. The PP offers a full day of strolling to temples, manicured gardens, and small handicrafts and clothes shops and cute restaurants, and is less crowded than the center of town. Also near some hiking trails if you're so inclined, though we didn't explore those.
6. In a related experience-maximizing vein, I believe Hyatt still offers the Diamond status test run (or whatever it's called, exactly) for 90 days (???). If you time that right with your trip, the Diamond status would get you complimentary breakfasts, room upgrades and perhaps other perks on your trip. We did that for our stay at the PHT (combining it with the aforementioned four free Hyatt nights); it made a memorable stay even more so, including providing us with a wonderful breakfast that otherwise would have cost a fortune! More information at whether this Diamond status deal is still available and how it works (including whether you can still couple it with a free nights stay) at the Hyatt forum.
7. Other unsolicited thoughts: a) The bullet trains are fun and impressive. b) the manicured gardens are incredible! c) We were very underwhelmed by the ryokan (traditional Japanese guest inn) experience, but that could have been because we picked a poor (though expensive!) one; if you do decide to shell out for one, do some research and book far in advance. d) I'd highly recommend the "Haunted Tokyo Tour" walking tour we took with an American expat woman who's lived in Japan for many years: http://www.hauntedtokyotours.com/ Despite the way it's billed at the website as "ghost walks", it is more of an explanation of Japan's spiritual life and exploration of some Tokyo back streets and neighborhoods, which are much more interesting that its main avenues.

As you can see, I can really wax enthusiastic about Japan! In addition to all of the above, the day to day way in which the culture operates is fascinating and impressive. Have a great trip!