I'd probably top up the BA & QF accounts until you have enough for a basic award, and then switch to AA (because redemptions are cheap and low fuel surcharges). Short awards on QF start at 8k miles oneway.

There are no 200% redeemable miles in business class, other than odd promotion. (200% status credits is earned on QF but that is no help to you).

Discount Y earning on non-home airline (and sometimes even on home airline) is rubbish. For example while QF business class has minimum mileage earn for your CE flights, the cheap ET flights only earn 25%.