There seems to be some misinformation in this thread about the new voucher rules. To be clear, if you have a new style Amex companion voucher, you do *not* need to start in the UK. You can start anywhere, including Frankfurt as mentioned by the OP.

But, the voucher can still only be used on BA, IB and EI operated flights. That means that to get all the way to Tokyo using the voucher, your options are indeed either via LHR or the new service on IB. There is no way to use it on JL for example.

As suggested upthread, you could could alternatively fly to another Asian gateway, but that will still involve a connection in London/Madrid (unless starting in SYD!) and then you would need a separate booking from the Asian gateway to Japan anyway.