On several occasions I've checked bags from JFK through to Asia with 4 or 5 flights, 2 PNRs, 2 or 3 airlines and conjoined baggage tickets. This also includes a couple of overnight layovers with bags retained somewhere in the airport for a morning flight.
Haven't had any problems yet.
Just check your bags through and don't worry about it. Priority tags typically work in Asia as well, unlike on our American brethren carriers.