😆😆😆

Because most pax on the Haruka will be in the same boat (plane) as you, having arrived on a flight that might not be on time. You will be buying a fare ticket and, optionally, a reserved seat ticket. The fare ticket (which includes the limited express surcharge) can be used on any train. The reserved seat ticket is, of course, for a particular train and I recommend buying one.

Looks like the last Haruka L'Ex would be around 22:16, and you will be able to get that even if your flight is hours late.
(Considering worst cases: There is a rapid train at 22:50 to Tennoji change to a loop line local to Osaka change to local to get to Shin Osaka. Another option is 23:09 getting to Osaka Station around midnight connecting to a local at 5AM to Shin Osaka. Don't want that. There might be late-night bus options. There is a hotel at the airport that am sure would have rooms available if all else fails. Don't worry, you will make the Haruka. Am just considering all options as I will be arriving KIX at 7PM in a couple of weeks).

At JR Kansai Airport Station, when you are buying your Haruka L'ex tickets, I am fairly sure that you could buy your shinkansen ticket and/or reserved seat for the following day. I say you can buy the shinkansen tickets when you get to Shin Osaka is because those Nozomi trains are very frequent and high capacity (and some originate at that station). Get reserved seats for the trip. If not available on the next train, then get the one 10 min after that, or 10 min after that. Ok, maybe 15 min for the train after next.

You can buy tickets from a human at both stations. JR staff at the service centers know enough railway English, if not fluency, to help.

You sh/could go to japan-guide.com for info on buying tickets of all kinds. They have lots of photos with their how-to.

For the above, I was looking at the timetable for Oct 14 at West Japan Railway Company - Timetables, Route Maps, and Station Maps (westjr.co.jp)

Or maybe you can get a digital ticket. Check at klook.com or the link below. Maybe print the QR code or use phone if you data plan for Japan.

The discount would, I think, would require a printout of the mco.

This puts the nail in the coffin to the idea of getting seat reservations in advance:

• · A handling fee equivalent to the Limited express ticket for each train will be applied to a reserved seating ticket after departure time.

Thanks again for all your advice. Just at the airport awaiting our flight to Osaka. 😁