Sorry I mean to say booking the alternative refundable using AA/BA/CX miles which is not part of JMB rules. But I'm not sure if JL system will detect the passenger name and automatically cancel still.
You risk having both bookings canceled in this case. I assume they know your FFP in the other program if you have ever redeemed or credited JL flights with those FFPs before. Not so hard for them to cross reference and create a customer profile with your personal info such as passport numbers.
https://www.jal.co.jp/en/inter/reservation/policy/
Japan Airlines may cancel any of bookings if customers have several bookings which cannot be actually used in terms of the itinerary
https://www.jal.co.jp/en/carriage/index_c006.html
(E) Cancellation of Reservations made by JAL
(1) JAL may, at its own discretion, cancel all or a part of the Passenger's reservations if two or more seats are reserved for the same Passenger and if:
(a) same section of routes on the same day are reserved;
(b) same section of routes on dates in close proximity to each other are reserved;
(c) different section of routes on the same date are reserved; or
(d) it is reasonably considered that the Passenger can not use all of the seats reserved.
...
(H) Personal Data
A Passenger agrees that his/her personal data will be furnished to JAL by the Passenger or his/her agent, will be retained by JAL or, if JAL deems necessary, will be transmitted by JAL to any of its own offices, other Carriers, the providers of travel services, government authorities or other entity or agency, for the purpose of making a reservation for Carriage, obtaining ancillary services, facilitating immigration and entry requirements or making available such data to government authorities or for any other purpose which JAL deems necessary in order to facilitate any convenience of the travel for the Passenger.