I don't have exact pricing info but I can tell you Russian AONE4 costs same as American. Canada and Australia would be cheaper, but you'd have to originate your trip from there to do it.

Here is an explanation about the rule for 1 transcon only in the USA.

WITHIN THE US/CANADA- 1 NONSTOP OR SINGLE PLANE TRANSCONTINENTAL FLIGHT PERMITTED.

TRANSCONTINENTAL FLIGHT IS DEFINED AS TRAVEL BETWEEN THE FOLLOWING CITIES:
BWI/BOS/FLL/BDL/MIA/EWR/NYC/ORL/PHL/SJU/YYZ/WAS

AND

LAS/LGB/LAX/OAK/SNA/PDX/SAN/SFO/SEA/SJC/YVR

So if you do BOS-SFO-BOS you already have too many "transcons". You could get one less transcon on your trip by doing JFK-DFW-HNL instead of JFK-LAX-HNL.

Which airports are you interested in seeing in the USA? You could also see much more of Australia if you have time.

You could do something like
MOW-HEL-JFK on Finnair or
MOW-LHR-BOS on BA/AA. Or take a longer LHR flights to deeper in the USA like LAX.

You get 4 segments in every continent except 6 in North America, unlimited stops except maximum 2 in the continent you start (europe). 20 flight numbers max. A single flight number is one segment, so your NRT-DPS is really two, since you have to fly NRT-HKG-DPS even if you don't stopover in HKG.

You could try MOW-LHR-BOS (2 months) - MSY - GCM - MIA - LIH // HNL - SYD - CNS - AYQ - PER - MEL - NRT - HKG - DPS - HKG - BKK - HEL(x) - RHO(stopover) - HEL(x) - MOW

Didn't use any Transcons, oh well ran into 20 segment limit. That's me trying to wear you out flying while taking you to nice places. New Orleans Grand Cayman Miami Kauai Honolulu Sydney Cairns Perth Ayers Rock Melbourne Tokyo Bali Bangkok Rhodes (very nice Greek Island).