Looks like the only partners at KHI are QR and CX.

Won't help you much for the outbound. Suggest you book to Bangalore (wide open) or Colombo (latter from LGW, no F?), then you'll have to pay cash to make you own way around and to KHI.

On the way back, most efficient is probably 15k pp in J (+£116 tax ) QR KHI-DOH (but ba.com won't recognise KHI!). DOH is lower mileage than India which helps but it look on the timetable you'll have 17hrs to kill in DOH.

There's no trick to this - with the one-jaw 241 (135k in F) you'll have to book any partner legs separately. This means the connections are at your own risk.