I believe SAS fly to Shanghai. They offer the best balance of convenience combined with points accrual offering 100% on all economy flights. It's also one of the quickest one-stop routings (LHR-CPH-PVG) - Copenhgen is very close to the great-circle track. SK long haul economy is supposed to be "OK". That'd be my first choice any day. They also offer reasonably priced Y+ upgrades (for which you get even more miles, I think)

At the other end of the "sensible routing" spectrum, you could look at Ethiopean. They also offer 100% on all economy flights but it's a LOT further and the connection times may not be great. Still, you could have an exotic stopover in Addis. ET even offer a free transit hotel, depending on your connection times and, of course, that longer routing will net you a lot more miles too. LHR-ADD-PVG-ADD-LHR gets you around 18,330 miles! They don't fly to Athens but you could go to, say, Rome and then take a cheap A3 connection to Athens. A plus is that you get to try their 787. A minus is that you get to try their 9-abreast 787

Personally, I would avoid 'Strikehansa' at all costs. I'm not sure if you've researched specific fares, but all the cheapest ones I can see are in K class which gives exactly ZERO miles! And as an extra insult, as a *G you don't even get a free extra bag, although their lounges are pretty good, especially the new one by the A380 gates at FRA.

Also don't forget Turkish. They have some fares with zero miles but some with 50% or even 70% although I haven't looked too deeply. A very convenient option for returning to Athens too. Also, the lounge at IST should be a must-visit location for any new *G.