Sorry, I've correct that now. The auto quote didn't work (neither did it just now) so I manually typed it; I guess I must have been confused.
Ah okey, so it sounds like this is only of real benefit if you want a fast train for one segment and a slower one for the other (paying for the Supplement onboard rather than in advance).
I'm arriving on Thursday the 30th September into NGO. I will spend two nights in Nagoya city whilst I meet a friend.

I then have from the 2nd October until Monday 4th October to get to KIX where I'll leave. Having wanted to visit Kyoto for some time now, I'm planning to travel to Kyoto during these dates.

I've been wanting to at least see something of Kyoto for some time now, so since I'm going to be nearby I decided to fit it into my schedule (in fact that's why I'm leaving via KIX instead of NGO). I like to think I'll be back again at somepoint so it'll be a short-ish visit this time, but I'll try to make up for that in the future; maybe seeing Nara next time too.

As you can see though I don't have much time to spend on the trains so I think the local stopping service is out of the question; happy to use a rapid service. I've not yet investigated the travel times the rapid requires compared to the expresses but it's on my list of tasks for the weekend. Of course, if the weather is nice and there is an interesting rural village along the railway line that's worth a wonder around for an hour or so, I'm happy to include that if time and schedules permit.
Thank you all again for your assistance.

Nagoya to Kyoto is not a long ride at all on the Shinkansen, less than an hour.

Similarly, Kyoto to KIX is only a little more than an hour on the Haruka Express. It costs about ¥3600.

All westbound Shinkansens from Nagoya (and they leave every 5-10 minutes) stop at Kyoto. The price for a one-way ticket is about ¥5800. You can also take a bus, but I'm not sure of the price or the schedule.

Leaving Nagoya early in the morning would give you plenty of time to sightsee in Kyoto during the day. There are no stops between Nagoya and Kyoto on the Shinkansen unless you take a Kodama (slower Shinkansen) that stops at Maibara and one other city whose name I forget. However, neither qualifies as a rural village.

If it's rural villages you want, you'll have to be content to view them from the train window.

Just 1 recommendation is to get a JR West Kansai Pass, which is 2000 yen for 1 day and covers the Haruka Express from Kyoto, making the express train way more affordable.

Just rent a bicycle in Kyoto and ride around the outskirts of town. You can find rice paddies just a few minutes out of Demachi-Yanagi Station...

If there are none on route there are none on route; I'll just stare instead :)

That's a great tip thanks! Shame my flight isn't until the evening. I'll remember that for next time too.
Cheers. Normally I take my own bike ;) - I hope to ride from Osaka via Kyoto to somewhere someday in the future. It really does allow you to see places you wouldn't normally find. ^

It saves you money at whatever time you leave.

I meant, it saves me money in the way I will use it, it would also save me money (even more) if I had the time to travel to and from some of the other places on the network.

So next time I'm in Osaka/KIX, I'll remember to plan my journey with the pass in mind.