My strategy would be to avoid UA as much as possible. LH has a much better C product in terms of food, FAs, etc. Also, with the new business class seats, the seats are much nicer. (I know you said you don't care about the seats, but I assure you that's because you've never flown longhaul before :-).) Note that on LAX-ORD and likely LAX-IAD, you'll get a two class plane where the classes are F and Y. This is domestic F though, and not nearly as nice as longhaul C.

Also, consider that ORD and IAD can be subject to snow/ice in the winter and thunderstorms in the summer. IAD is particularly worth avoiding. Go over to the UA forum and do a search for IAD, and you'll see complaints about everything from the security to the building itself to the UA employees. (Though people say it's been improving this year -- I haven't had a chance to check it out myself.) So, I'd avoid ORD/IAD as there is always a risk of missing a connection, and these airports probably highten that risk.

If it were me, I'd go with the fewest changes possible for this reason. (And 6 hours in the MUC lounge isn't that bad -- bring a few books or DVDs and a laptop that plays them.)

Since you're not a frequent traveller, you probably don't care about miles. But, you will get more miles with the stop in ORD/IAD.