It's not how full the flights are:
On 20 March, BA11 is
F5 A2 J9 C9 D9 RC IC W9 E6 TC Y9 B9 H9 K9 M9 L9 V9 S5 NC QC OC G0
BA15 is
F0 A0 J9 C9 DC RC IC W9 E5 TC Y9 B9 H9 K9 M9 L9 VC S5 NC QC OC G0
On 25 March, BA16 is
F4 A0 J9 C9 D4 RC IC W4 E1 TC Y9 B9 H9 K7 M4 L2 VC SC NC QC OC G0
That's a little fuller, but BA12 is similar to the flights on 20 March.
F7 A0 J9 C9 D7 R1 IC W9 E9 T5 Y9 B9 H9 K9 M9 L9 V9 S5 NC QC O3 G0
This is all down to the Saturday night stay, and those fares not being offered without one unless you do a holiday.
Personally I'd either choose QR ex-EDI or NCL-LHR-SIN on a BA holiday booking, rather than connecting to T3 at LHR and again in DXB. However, while you wouldn't earn many TPs (50TP and something like 3,000 avios) this is an exception to the general rule that non-BA, OW codeshares on non-OW metal are non-earning.