Frances,
Along with the OZ Carnet issue (much easier to use the method Warin suggests),
you should know/ be reminded that you canNOT import your R12GS into the USA--"permanently," to eventually re-register it there--UNLESS the 12GS is/ was originally manufactured to USA (DOT safety, and EPA emissions) specifications.
I don't know whose/ which vehicle specifications are required by the
Phillipines, or used by the BMW importer in Manila. But you definately need to check in advance.

US government vehicle specification "conformance" is identified by an embossed metal plaque on the motorcycle frame installed at the time of original manufacture in Germany. The plaque will actually use the language to the effect that the particular bike VIN was manufactured in accordance with US government "FMVSS" (Federal Motor Vehicle Safety Standards), etc.
If the Phillipines uses USA standards, and your bike has this USA standards plaque, no problem to import it into the US.
If the Phillipines uses different vehicle standards, e.g. Euro, OZ, or its own,--and you attempt to import the 12GS to the US by seafreight or airfreight--US Customs will either seize the vehicle, or force you to reship it to OZ.
There is technically a procedure available to "conform"/ change non-US vehicles to US standards, but this procedure is practically speaking unworkable and would cost you more than the 12GS is worth, even if could get through the US legal/ bureaucratic hoops.
For the sake of your overall plans, you MUST check on which national standards your 12GS was manufactured to, and if not originally US standards, give up plans to bring your bike to re-register in the US.
Good luck.