While I haven't taken the flight, people report good success upgrading the LH nonstop between PDX and FRA.PDX-FRA-CPH seems far and away the easiest routing to me.

That said, you won't be able to confirm the upgrade in advance. Since you are flexible with your timing and have enough time between now and your trip, you should be able to find a time when you can fully confirm the upgrades at the time of booking.

While LHR is no fun for the connection, it will give you the greatest number of options from the US -- i.e. PDX-DEN/SFO/ORD/IAD-LHR-CPH. If you can book the DEN option and confirm the upgrades, this would probably be the preferred way and there are bonus miles on the DEN-LHR flights.

Alternatively, if you wanted to try out the new C seats, you could book PDX-IAD-ZRH-CPH. This isn't necessarily the fastest route, but ZRH is a great airport to transit and this would get you into the new C seats.

You'll probably need to book this trip by calling 1K reservations. Luckily as a 1K there is no booking fee. Before you call, I recommend doing some research to find out the routing you'd like to take; especially with non UA cities like CPH where there are an unlimited number of routing possibilities, the agents aren't necessarily sure what the best routing is. This is why it helps to have suggestions. You can also use a seat like seatcounter.com to determine how full the flight is and if there are any upgrade seats available (shown as I booking class on seatcounter).

Then, you need to call United to:
- Determine if there are upgrade seats available on the flights you want
- Book an upgradeable coach fare (cheapest fares do not qualify)
- Have the agent confirm your upgrade.

You didn't mention how important price is for you -- if you are price concious you could look into booking two tickets -- one to LHR and another onto CPH. That may or may not be cheaper than booking together.