It is possible to use IB+ to book JAL flights, but the IB+ and BAEC websites often find different availability for OW award flights in general (and many times flights are available to book that don't appear online).

However, even if you can book those flights over the phone it is probably better to do it with BAEC (your avios can be transferred there for free), because IB+ redemptions on non-BA OW airlines are not refundable.

If your travel plans are set in stone you may call IB+, use the local rate number in a sticky on this forum (maybe the surcharges are lower with IB+ than with BAEC, as happens with AA flights, I don't have any experience with JAL). In my experience I am talking with an agent within seconds every time I call IB+ (although I call in Spanish, which I'm sure makes things much easier).