Indeed, the cheapest flights were on Skyteam carriers, but LH was offered for marginally more. Even the LH tickets were a great deal. That isn't the point, however. I suspect the same inexplicable gulf in charges will be the same, no matter the carrier. For the dates and times I needed, the LH tickets were $2730/all in, which is the lowest I've seen in months of watching the fares. FWIW, Skyteam was $2400.
Update: after 90 minutes on the phone with two agents and escalating to a supervisor, I was able to get them to acknowledge I was overcharged by $622 and they agreed to a refund.
Good for you. Make sure you keep all their names on file until you see the correct amount on your credit card bill.