ITK.....either log it like you have done in CAA/JAR/JAA/EASA land OR do per FAR's. Your pick....but when a Log Book Audit is done by the CAA et al....they will look to see it logged their way in their format and in their style Logbook.
If you log it using the FAA method....you might encounter a problem breaking out the right hours to suit the CAA et al.
My impression is you are trying to force the two methods into one...and that dear chum just doesn't fly in either system.
Simple rule for the FAA....if you are doing the driving....either with hands on the sticks or pushing autopilot buttons.....Log PIC.
You want interesting questions.....ask how many Pilots can log PIC simultaneously in the same aircraft!
Or...must you have a current Medical Certificate to log flight time?
Better yet....what if you have neither Medical Certificate or License of any kind....can you log flight time?
We can really get you confused with not a lot of effort!