Well, as you'll fly paid J all the time the "status benefits" are quite small anyway:
1. F lounge access (+F check in, which is a minor benefit) at BKK/LAX so just make sure you'll have OW Emerald status
2. with AY you cannot get upgraded from J, with BA there's the option/small change to upgrade/be upgraded to F
3. With AY Plat you can use the Spa at HEL, if that means anything, most likely not
4. With AY Plat you'll earn upgrade vouchers which are valid on AY metal only, if those have any value to you
-->I'd choose the program that you want to use your miles with