You could do it with 2 overlapping RTWs, if you've got the time/money/interest.

The first RTW begins in Oz in January, and you start out going Oz to BKK. Now you buy and begin your 2nd RTW (the 1st is still active, as a layover in BKK).

The 2nd RTW begind in BKK, goes to MNL and then to LHR. At this point, if you have the time, you could take side trips to Dubai or wherever, then on to North America and then back to Brizzy. In March, you complete the 2nd RTW by going from BNE to BKK, where you resume the 1st RTW. The 1st RTW then goes to TPE and your stops in the US before heading to Europe and then home (without stopping in Asia).