DONE3 Europe help
 

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.

What about someplace else in the Middle East?

You could do JFK-oAMM-xMAD-xLHR-oMCT-xLHR-SIN or substitute DXB for MCT. If you wanted just to do the LHR-MCT turnaround (really not a bad experience) you could add a day in AMM, since LHR-MCT departs in the morning, and MCT-LHR leaves at midnight. That would give you 5 hours in the T5 arrivals lounge to shower and nap before heading to T3 for the Qantas flight.

(AMM-xMAD-LHR on 19 October, LHR-xMCT-LHR on 20 Oct. returning 0645 on the 21st, then LHR-SIN.)

So stop in Amman and maybe stop in Muscat (or Dubai or Abu Dhabi)?
I did a turn through DXB last year (HEL-LHR-DXB-LHR-HKG with bags in storage at LHR T3 instead of checking them LHR-xDXB-LHR). Is the MCT turn the same sort of thing?
I had been trying to avoid a terminal change at LHR, but I guess it's unavoidable with the flight schedules through the cities I've been looking at.

Yes, I did the same thing with MCT - left bags at the T5 storage facility, did the overnight turn, then after using the arrivals lounge (landside) took the train to T3 for an onward flight (AA in my case). No big.