A great many thanks to everyone for your very insightful input. For my part, I'll say that I've come to the following tentative conclusions after reading your responses and doing some additional research on the JR West and JR Central websites. Notably,
jib71 put his finger pretty much on the dot of the hotels we're considering in Osaka and Kyoto.
We'll probably want to take the Haruka KIX-Shin Osaka, then backtrack to Osaka Station. That is, unless you'd advise (based on the time it takes to backtrack, hassle of changing trains, distance of walk from Osaka Stn. to RC vs. cost of taxi from Shin Osaka to RC) just taking a taxi from Shin Osaka to the Ritz.
For Osaka-Kyoto, a Shinkansen is probably overkill. Only reasons to do it would be for space in the Green Car and foreshadowing the full-blown Nozomi treatment to Tokyo four days later. So for that, we'll probably take a JR train or other private train.
Don't think we'll need to use JR trains or private trains to get around Kyoto. We're young and we love to walk everywhere. The Kyoto subway and a few taxis should take care of us. That said, if we buy a pass, we might as well put it to use.
Then it's JR (or other private rail?) to Nara and back for a day. Scheduling of the day trip might be dictated by whether we buy a JR pass (such as a 4-day pass) that covers the Haruka, Osaka-Kyoto, and Kyoto-Nara-vv. That will in turn be driven by price. I've read in another thead in the Japan forum that buying the pass can be cheaper than a simple KIX Haruka ticket, so it might make sense.
After all that, it's the Nozomi to Tokyo. I expect our hotel will be around the Imperial Palace area, or maybe in Ginza, so we'd likely just take a taxi from Shin-Tokyo to the hotel. Finally, N'Ex out to Narita.
That's a lot of trains. Good thing I enjoy trains as much as planes. Good trains, that is, like they have in Japan.
Thanks again to all. Arigato!