You heard wrong. While it is true that status (best if combined with premium cabin tickets) helps to get somewhat more leeway by airline staff when it comes to getting on more and bigger bags into the cabin of an aircraft, all the major airlines and airline alliances officially only award extra checked bag allowances to their frequent fliers but not more carry-on baggage allowance.
Status or not, bringing on more than two bags is pushing it almost anywhere. You may be successful sometimes, sometimes you may not.
Between LAX and TYO/ICN, you have the choice of
AA/
JAL (oneworld),
UA/
ANA/
OZ (Star Alliance) and
DL/
KE (Skyteam), and none of them has extra cabin baggage listed as status benefit.
The best way to ensure your costly and fragile gear will travel in the cabin is talking to the airline in advance and purchasing an extra seat for your equipment, like most/all airlines offer for musical instruments and the like. Be aware of restrictions on electronics, specifically batteries which are allowed only up to a certain capacity.
Also, all major airlines have policies in place for members of the media (see
AAs here, for example), so establish yourself as such (via your FFP profile) to profit from them. This will also help with getting gear accepted into the cabin that usually is not.
edit: keep in mind some airlines have weight limits for carry-on luggage. For example, ANA, JAL and Asiana only allow 10 kgs and Korean grants 12 kgs, whereas the US airlines do not have weight limits in place, only size restrictions. I haven't seen them enforced at any of them (among the large airlines, only LH and LX are notorious about this in my experience - I've witnessed top-tier status fliers who had to check their overweight bags in Frankfurt) but they're in place nonetheless.