Plotting out a DONE3 (Asia-North America-Europe-Asia).
I have North America and Asia sorted out, but Europe is proving to be a headache.

At the moment, I’ve got:

JFK-AMM RJ0262 2230-1645+1 OCT 16
AMM-DME RJ0177 1045-1545 OCT 18
DME-MAD IB3811 1805-2115 OCT 19
MAD-HEL AY3184 1010-1530 OCT 20
HEL-LHR BA0795 0755-0905 OCT 21
LHR-SIN QF0032 1205-0805+1 OCT 21

I had been hoping to stop in Amman and Moscow, but the flight schedules aren’t lining up as well as I would have liked (DME-MAD-HEL-LHR would have been a mileage run aimed to arrive into LHR T3 in time to get QF32).

I’d like to stop in one or two places that I haven’t been to before (I’ve been to London, Rome, Madrid, Frankfurt, Berlin, and Amsterdam. Have been to Paris and Helsinki, but spent most of my time there in hotel room with a migraine) while maximizing mileage/status credits.
I would prefer to leave Europe on QF32 due to its arrival time in Singapore.

Any ideas/suggestions?
Help please.