A couple of options come to mind.

1) If the dates line up, you could fly Icelandair SFO-KEF-AMS in Saga Class for $2,400 a person. It's not lie flat business, but it's a lot better than 9 or 10 across coach in the back of a widebody.

2) Somewhat surprisingly, Google Flights offered up Air Canada / Jet Airways SFO-YYZ-AMS for 2,400 a person for some dates in October. Jet Airways is lie-flat business although I have no idea what it's like otherwise. There is a nasty 17 hour overnight layover on the return, though.

I hate 10+ hour flights in coach, but I'm still not sure how far out of the way I'd go vs a non-stop coach flight. a connection sure. overnight layovers, not so much. But that's a personal call.