I was about to say something similar to guv1976, make sure you check the cost from QR Avios in addition to BA Avios. BA's online booking system often returns no availability for any flights that require a connection, especially if the connection isn't in a straight line (for example I was searching for CAI-NBO the other day, BA would not show me the QR flights that were available via DOH but both AA and QR did have them). QR also has a lower Avios cost on JL and CX flights, but might have higher cash fees, you'll have to weigh the difference. Also QR doesn't have JL in their online booking engine, you have to call or chat for JL redemptions which has an additional fee.

For lounges, since you're BA Gold you'll get access to the first class lounges in most places (Not DOH, as that's not a OW status lounge). The Al Mourjan (business) lounges in DOH and the CX First lounges are definitely worth a long-ish layover for (CX has a spa with complementary short massages). But for JL, their excellence is in the sky, their lounges are pretty ordinary and often quite crowded (lots of credit card status customers in Japan) so these days I don't look to spend any more time than necessary in them (I live in Japan so see them A LOT). Another poster mentioned the MH lounge in KUL, which the Emerald lounge (they call it Platinum lounge) is actually quite nice with a very tasty a la carte menu and sit down dining. QR also has outstation lounges in SIN and BKK that are both excellent, you can only access them on business class tickets (from any OW airline), similar to DOH they are not status lounges.

Sounds like you have some exciting travels ahead. You won't go wrong going long haul with any of JL, CX, or QR. Within Asia however both JL and CX have some pretty tired aircraft. You'll want to avoid JL's 787-8s which have angle flat business class, and CX has a ton of 777-300 (not ER) and A330's in their regional configuration which is just a recliner. So those will be a let down if you book one without knowing. I'll throw MH into the pot as well, a lot of people love to hate on them, but I have always had really excellent service with them. They operate mostly 737s in the region with standard recliners up front, but TYO and SEL both get A330 and occasional A350 service. I fly the KUL-NRT route once or twice a year and will actually choose MH metal over JL if it's available. (which is exactly what I'm doing in January 2026, JL code on MH metal)