The lack of a codeshare doesn't really matter.
For a RTW ticket you would need a 3rd stop, and I believe a 10 day minimum. The latter should not be difficult but the former may be. And if you are going to fly J the whole way it is probably cheaper than actually buying the segments in question.
If you did it as a redemption I believe it would either be a RTW redemption or a US-Europe + Europe-Asia rather than a single reward.