Travelsig,
even the RTW allows you certain backtracking.
What works quite well if you need Asia only is to start west bound on LH 456 from FRA to LAX arriving at 12:40 and connecting to SQ 11 to NRT / SIN leaving at 14:45. On arrival hardly anyone at immigration in LAX and thus easy to enter and leave again - getting you to NRT at 18:05 next evening. Some hours more - but not overly many.
And then schdule your hops accordingly from there throughout Asia / Oz
Cheers
Thomas