Yes, BA should have flat beds to NRT.
As an alternative to boosting the miles balance, don't forget that you could buy a World Traveller Plus ticket and upgrade to Club using 40,000 BA Miles, subject to award space availability.
Whether this is worth it for you will depend on the relative prices of the Club and WT+ tickets you can buy for money (and with whatever flexibility you need or don't need), plus the value to you of the 40,000 miles in terms of whether you spend them now, or keep them and add to them the miles that you'd earn flying paid Club.
Sometimes, a cheap WT+ ticket and Miles for Upgrade to Club can be absolutely outstanding value.