Two comments -

First, there are some new people at the RTW desk, so I would phone back and ask for a supervisor. I just talked to one yesterday (very nice person) who needed to check if a NA-Asia-SWP-Europe route wasn't "backtracking" between Asia and SWP.

But second, I'm not sure that I don't agree with them on your itinerary. Originating in NA, it would seem to me that the "second entry" exception, which limits one of the two entries to transit-without-stopover, is moot, given your proposed multi-segment plan once you return. The interpretation of the transit-without-stopover rule now appears to be firm in that only one NA touchdown is allowed; i.e. GRU-xJFK-HKG might be okay, but the 2-sector NA passage isn't.

If you get clarification on this through a phone-back, please post the results.