The limiting factor here really is the issue of the voucher. There are only 12 days a year that you can trigger a voucher (your card statement days), choose very carefully which one. Pick the first statement date that is less than 365 days before the last day you could wish to start your journey.

You can speed up the voucher-obtaining process (it does arrive very quickly by post though) by phoning Amex once the statement is issued and getting the voucher code number over the phone from them.

Then:

(A) If you get the voucher <365 but >350 days before the desired travel date, watch availability closely and phone BA first thing on day T-349. Unfortunately here you are at the mercy of non-Amex-241-holding redemptionists, who can book their trips as two one-ways. You, on the other hand, cannot book until the return (any return) opens up. Hence T-349 not T-350.

Get the right outbound flight and any return flight, then watch the return availability closely over the next week or two until your chosen flight appears, and phone BA and change the return date on the ticket for free.

(B) If you get the voucher <350 days before your planned travel date, just get on with it!

(I am assuming the 350 day advice is 100% correct and that it is not possible to get tickets at e.g. T-355.)