JR East reserved seat at Shin-Osaka

My friends and I (who all have nationwide JR passes) are planning on going by shinkansen from Shin-Osaka to Shinagawa, then transferring there to the Narita Express. Would we have to wait until Shinagawa to make our seat reservations for N'EX, or could we do it at the ticket office at Shin-Osaka?

More generally, is it possible to pick up reserved seat tickets for JR East from a ticket office in JR Central's territory, and vice versa?

You can reserve both your trains at Shin-Osaka with the JR Pass.

Nationwide Japan Rail Pass is issued jointly by all the six JR regional passenger railway companies.
So, your Japan Rail Pass, as long as it is valid, can be accepted at any JR ticket counter.

When will you travel?
What airport will you fly into?

More generally, is it possible to pick up reserved seat tickets for JR East from a ticket office in JR Central's territory, and vice versa?

Basically it is doable.

Major exceptions
: When you have reserved a seat through a system of one or a few particular JR regional companies, you should visit a counter of the JR company who joins the system.
: When you plan to use a JR pass (other than Japan Rail Pass) for your train ride, you should visit a counter where that JR pass is accepted.

The non-Shinkansen zone of Shin-Osaka Station is managed by JR-West.
The Shinkansen zones of Shin-Osaka and Shinagawa Stations are managed by JR-Central.
The non-Shinkansen zone of Shinagawa Station is managed by JR-East.

I fear omotenashi's answer is unnecessarily confusing regarding the exceptions for advance reservations.

What you need to know is that you can book a ticket on any JR train that enables you to make a seat reservation at any JR ticket office anywhere in the country (up to a month in advance) with your JR pass. That is, once you actually have your pass (rather than before you have your pass), you can book your reserved seats at a JR ticket office and you can book Shin-Osaka to Narita Airport - the staff will make the reservations for you and issue with the reserved seat tickets.

You cannot reserve and receive a ticket in advance for a train that does not require reservations like a local commuter train (eg, the local trains from Osaka to Shin-Osaka). In those cases, your JR pass gets you onto the train and free seating/no allocated seats applies.

For an example of booking "out of area", I booked all my JR Hokkaido rail travel in the JR East area (both my paid tickets and the seat reservation for my guests who are using JR passes) when I was last in Tokyo. Similarly, from Akita last week I booked a bunch of Tokyo to Osaka tickets for July in advance for someone and sent the tickets to them by post (because they are not even in the country yet).

The six JR regional companies have their common system
to process seat reservations and issue tickets at JR ticket counters,
so Japan Rail Pass travelers mostly do not need to know
which JR section is operated by which JR company.

unnecessarily confusing regarding the exceptions for advance reservations.

Regrettably here is no hint given
to suggest how it may be confusing (or to resolve that possible confusion).

Anyway, I should clarify that part of my previous response:
it is about a JR Internet seat reservation system for train rides in the designated zone(s).

There are 5 ways.
1) Arrive in Japan and make a reservation at the time of Pass exchange.

2) After arriving in Japan, make a reservation
when you have time at nearest JR station where has ticket office.

3) Before departing Japan, make a reservation at JR-East site(online),
ticket reciving at pass exchange if in JR East or at Shinagawa station on the day.

4) Reserve in Shin-Osaka on the day or in advance.
(either in JR-Central or JR-West staition's ticket office)

5) N'EX will rarely be occupied except for some super busy seasons,
so you can order the conductor in the car.
(Although, until the revision in March of 2015, needed a "reserved seat ticket" in advance.)

It is easier to transfer at Shinagawa station than the end Tokyo station.
http://www.jreast.co.jp/e/stations/e788.html

Personally, it is more efficient to change to a plan to depart from KIX
or to flight from KICX to NRT by cheap domestic flight (LCC) if on weekdays except Friday.
https://www.kansai-airport.or.jp/en/
https://www.skyscanner.net/

Anyway, I should clarify that part of my previous response:
it is about a JR Internet seat reservation system for train rides in the designated zone(s)
I thought that was what you were referring to, as the reservation in advance system is not comprehensive and regionally based. But the OP has a rail pass, so that didn't really apply in this case.