You log the hours as per the law that you are flying under. So if in this case you can only log 50% that's what you log, any other hours claimed is pure and simple fraud. As long as that is what the legal hours required by your state of work you can not legally claim more, regardless of your nationality or you next employers rules. Once you fly under a different states laws you may log differently. How we all feel about that and the fatigue issues is a different argument.