And the transit through Asia does not need to be a single-plane through service (such as BA10, QF9, QF1 etc). It can be a valid connection, but must be transit and not stopover in Asia. So you can use something like QF51 BNE-SIN connecting to QF9 SIN-LHR. You can even use CX flights connecting in transit in HKG and changing planes and flight numbers.

Transiting Asia a second time does not require Asia to be counted twice in the continent count.