You are correct, you can have more than 4 transfers in the USA in your ticket ex OSL. The LH RTW-Desk *should* know this but apparently the agent replying to your e-mail does not:
15 TRANSFERS PERMITTED ON THE PRICING UNIT.
4 PERMITTED TRANSFERS BETWEEN INTERNATIONAL
FLIGHTS WITHIN THE FARE ORIGIN COUNTRY
WITHIN ANY NATION
4 PERMITTED TRANSFERS BETWEEN DOMESTIC
FLIGHTS WITHIN THE FARE ORIGIN COUNTRY
WITHIN ANY NATION
UNLIMITED PERMITTED AT ANY POINT.
DOMESTIC FARE BREAK SURFACE SECTORS PERMITTED ON THE
FARE COMPONENT TO DESTINATION FARE BREAK POINTS.
5 EMBEDDED SURFACE SECTORS PERMITTED ON THE FARE
COMPONENT WITHIN AREA 1 BETWEEN AREA 1 AND AREA 2
WITHIN AREA 2 BETWEEN AREA 2 AND AREA 3 WITHIN AREA 3.
NOTE - TEXT BELOW NOT VALIDATED FOR AUTOPRICING.
SURFACE SECTORS-
- INTERMEDIATE SURFACE SECTORS PERMITTED AT
PASSENGERS EXPENSE.
- IF SUCH AN INTERMEDIATE SURFACE SECTOR IN
ITINERARY EXCEEDS 24 HOURS IT IS
CONSIDERED AS ONE STOPOVER.
- MILEAGE FOR SURFACE SECTORS MUST BE INCLUDED IN
THE MAXIMUM PERMITTED MILEAGE CALCULATION.
- IF A SURFACE SECTOR ATTRACTS MORE THAN ONE
TPM THE LOWER APPLIES.
- NOT MORE THAN 5 SURFACE SECTORS ALLOWED.
THE CITIES ON THE IATA LIST OF CITIES WITH
MULTIPLE AIRPORTS /SEE IATA PASSENGER AIR TARIFF/
SHALL BE CONSIDERED ONE CITY.
---------
SURFACE SECTORS AND MULTIPLE AIRPORT CITIES
REQUIRE A SEPARATE COUPON
--------
FIRST CONTINENTAL CROSSING ON THE ENTIRE JOURNEY
AS DEFINED IN THE RULE APPLICATION OF THIS FARE
MAY NOT BE A SURFACE SECTOR. SUBSEQUENT CROSSINGS
BETWEEN CONTINENTS MAY BE SURFACE SECTORS.
---
TRAVEL THROUGH THE CITY OF ORIGIN IS NOT PERMITTED
--
MAXIMUM OF 4 INTERNATIONAL ARRIVAL AND DEPARTURES
IN THE ONE COUNTRY
OR - 15 TRANSFERS PERMITTED ON THE PRICING UNIT.
4 PERMITTED TRANSFERS BETWEEN INTERNATIONAL
FLIGHTS WITHIN THE FARE ORIGIN COUNTRY
WITHIN ANY NATION
4 PERMITTED TRANSFERS BETWEEN DOMESTIC
FLIGHTS WITHIN THE FARE ORIGIN COUNTRY
WITHIN ANY NATION
UNLIMITED PERMITTED AT ANY POINT.
DOMESTIC FARE BREAK SURFACE SECTORS PERMITTED ON
THE FARE COMPONENT TO DESTINATION FARE BREAK
POINTS.
5 EMBEDDED SURFACE SECTORS PERMITTED ON THE FARE
COMPONENT WITHIN AREA 1 BETWEEN AREA 1 AND AREA 3
WITHIN AREA 2 BETWEEN AREA 2 AND AREA 3 WITHIN
AREA 3.
NOTE - TEXT BELOW NOT VALIDATED FOR AUTOPRICING.
SURFACE SECTORS-
- INTERMEDIATE SURFACE SECTORS PERMITTED AT
PASSENGERS EXPENSE.
- IF SUCH AN INTERMEDIATE SURFACE SECTOR IN
ITINERARY EXCEEDS 24 HOURS IT IS
CONSIDERED AS ONE STOPOVER.
- MILEAGE FOR SURFACE SECTORS MUST BE INCLUDED IN
THE MAXIMUM PERMITTED MILEAGE CALCULATION.
- IF A SURFACE SECTOR ATTRACTS MORE THAN ONE
TPM THE LOWER APPLIES.
- NOT MORE THAN 5 SURFACE SECTORS ALLOWED.
THE CITIES ON THE IATA LIST OF CITIES WITH
MULTIPLE AIRPORTS /SEE IATA PASSENGER AIR TARIFF/
SHALL BE CONSIDERED ONE CITY.
---------
SURFACE SECTORS AND MULTIPLE AIRPORT CITIES
REQUIRE A SEPARATE COUPON
--------
FIRST CONTINENTAL CROSSING ON THE ENTIRE JOURNEY
AS DEFINED IN THE RULE APPLICATION OF THIS FARE
MAY NOT BE A SURFACE SECTOR. SUBSEQUENT CROSSINGS
BETWEEN CONTINENTS MAY BE SURFACE SECTORS.
---
TRAVEL THROUGH THE CITY OF ORIGIN IS NOT PERMITTED
--
MAXIMUM OF 4 INTERNATIONAL ARRIVAL AND DEPARTURES
IN THE ONE COUNTRY
You could try again with the LH desk pointing to this section of the fare rules or reach out to a travel agent familiar with RTW tickets, there are quite a few here on FT. You don't need a TA based in Norway.
If you plan on doing *A RTWs regularly, perhaps you can find a way to originate your travels in Japan, the CRWSTAR1 is $4523 plus tax (I didn't see the CRWSPCL in the fare list on Experflyer).