Relatedly, should we take the Nozomi from Osaka to Kyoto? Or would we be better off buying a Kansai-area JR rail pass for four days or so that would cover our KIX-Express, Osaka-Kyoto, and Kyoto-Nara side trip? Can we reserve a Green Car on those trains? Am I correct that, because of the non-Nozomi rule for JR passes, we'd be on a Hikari for Osaka-Kyoto?
The JR West Kansai Area pass covers
NONE of the Shinkansen routes between Osaka and Kyoto.
You could however take the Haruka (Airport train) from Osaka-Kyoto with the the pass. However, both the Shinkansen and Haruka depart from Shin-Osaka Station, not Osaka Station.
Another note is that you don't even need to step foot on the Shinkansen to get from Osaka to Kyoto. You can take the JR Rapid train that departs from Osaka Station to Kyoto Station.
Alternately, there are Limited Express trains on Hankyu Railways from Umeda Station (next to Osaka Station) into Central Kyoto. (the cheapest option but just as fast depending on where you want to end up in Kyoto).
If you do have luggage these trains do get busy so that would certainly be a problem, but can be a bit easier if you decide to stay in either Kyoto or Osaka for 5 days in stead of the 2/4 split, this way, the day you arrive you can take ie the Haruka Limited express to Kyoto, check in your hotel and store all your luggage to the day you check out to Tokyo. If it were me I'd consolidate the hotels in Osaka and Kyoto into one, either in Osaka or Kyoto, the cities are close transportation wise, i'd be a pain the day you have to check out, carry your luggage on transportation to re-check in, plus the time lost.