AFAIK MSP-AMS is operated by both A330 and 767-300 aircraft, depending on the time of day. The problem might be that AMS-BHX on KLM has good connections to only one of the non stops. You could try to search by schedule and pick the 767 segment since international connections can be as long as 24 hours. How would you feel about a night in Amsterdam?

MSP-CDG had been the horrid 767-300, but I think it used an A330 this summer. There might be some seasonal possibility of this route reverting to the 767.

Another idea would be to fly TATL into MAN and take ground transportation.

However, I wonder why the OP wants to avoid the A330-200? I think it's a nice plane, with good nose to tail AVOD. The aircraft generally still look new and fresh. To me, it's MUCH MUCH MUCH than a nonreconfigured 767-300 or non reconfigured 747, although clearly inferior to the 777. However, there are some tricks to getting comfy in the angled flat seats.