I think we can, as a starting point, understand what objectively happened is this:
Dale Cooper prevents Laura from being murdered. She gets sucked into another timeline, dimension, or story. Dale Cooper crosses over with Diane to that dimension and awakens as a different character in a different story with different plots already in motion. He finds Laura Palmer, but she's not Laura Palmer anymore, so it doesn't matter.
The conclusion we see is a conclusion to a different story. Imagine Twin Peaks ended when Cooper and Diane drove through the electrical barrier and episode 18 was an episode of a show called Odessa.
What stands out to me most dramatically is that the Cooper that emerges from the Lodge and travels with Diane is very still, discourteous, and robotic. I don't think it's the real Dale Cooper. Although he exhibits some moments of earnestness, overall, he is dark and inexpressive. I think this character is the doppelgänger.