...lots of good advice..... using points here's what I've been able to put together.....

arrive KIX 5pm (from IST)... 2 nights at Osaka Hyatt, since it's relatively close to KIX airport, and have a day to explore Osaka

2 nights at Marriott-Associa Nagoya Station
enjoy a 2pm Drogons baseball game in Nagoya Dome
train trip to the Takayama forest-mountain area
other signtseeing for ceramics and art in Nagoya area
(as mentioned, a wonderful use of the Cat 1-4 e-certs!)

6 nights at old Hyatt near Shinjuku station
see Giants game at Tokyo Dome

1 night again at Marriott Nagoya station
(because no availability for free nights in Tokyo or Osaka or Kyoto)
Maybe just use Nagoya has a quick overnight...leave Tokyo late on this Sunday night and be in position to go to Kyoto on Monday morning

3 nights Kyoto....closest hotel at a reasonable price for a Western-style place was Reiah Hotel Otsu at Ishiyama station, about 4 stops (15 mins) away from Kyoto on a JR regional line


Final night
Hyatt Osaka, since it's closer to KIX airport (and free) to catch a noon flight the next day.....any experience on how early we need to be at KIX to catch a noon flight to ICN (then on to LAX)?
Maybe a Tigers 6pm baseball game at Koshien outdoor stadium this last night?

.... other suggestions? thanks to all!