So you are planning to fly that RTW on a paid ticket, accumulate more miles with SOF-Germany flights and then redeem those for an award to North/Central America for as few miles as possible?
For that scenario, I'd say AA is the best choice. They have off-peak awards to North America (US, Mexico) for 40,000 miles return. Central America with a stopover in the US in any of their gateway cities (JFK, ORD, MIA, DFW, LAX, or any other with service to Europe like RDU or BOS) is 70,000 miles return, though.
Check the AAdvantage earning charts for the airlines you'll be using on your RTW trip and select carriers and qualifying fares that'll give you full miles.
The same applies for those SOF-Germany flights: You have the choice of AB and BA. BA will earn 100% mileage on all fares (even the cheapest ones) in the AAdvantage program, while AB's cheapest buckets will only earn 25% mileage.
You'll likely manage to get enough miles for a North American AA award with some mileage maximizing on that RTW and two flights to Germany via LHR.