If you can keep a mailing address in Europe, I would suggest to enroll in CO Onepass (and ask for a comp possibly, using your Star/ Oneworld status).

European Onepass members get a 100% bonus EQM on Business Class flights (while US based members only get 50% bonus).
In addition, European Gold and Plat do receive a CO Presidents club membership - this is a non published benefit but I have been getting it for 4 or 5 years now. You would get lounge access without any restriction (i.e. no "same day int'l flight on skyteam partners" requirement) and you can bring one (maybe 2?) guest.

Another poster suggested to stay on the FB program but you would get less Elite bonus miles. CO offers 100% for Gold/ 125% for Gold.
Given your heavy travel pattern, this would make a considerable difference in miles at the end of the year

As a CO elite (Silver/Gold/ Plat) you would also be able to get free US domestic upgrades on both CO and NW (only Gold & Plat FB elite get upgrade on NW; not sure about upgrade possibility on CO).

Only downsides - 50% EQM on cheap fares, including many partner airlines (except if you book them on CO.com) and lack of awards availability (but YMMV - just my own experience on the routings I want).

NW Worlperks would be my 2nd choice, but no free WP lounge membership (except Asian members), J/F EQM bonus is 50%,

However, you get 100% EQM on all fares (including cheap fares on many other partners).

And much better awards availability (again - personal experience -YMMV) and great non Skyteam partners (e.g MH, Air Tahiti Nui, with F awards possible). In some cases I was able to find J awards on KLM operated flight while both FB/Onepass did not show any availability on the same flights...