I have a canon character for each game too. The others, while I still RP them, are more like "What if" playthroughs or alternative realities. They're not less important, just different decisions that may have taken place. I like to think of it like the alternative endings to the movie, "Clue."
"Here's how it could have been, but this is what really happened."
Me too. This is how I do it as well. I have a 'canon' playthrough in all of the games that serves as my main import data. And I have a back-up canon playthrough where I make a bunch of 'alternate' decisions to see how different the game can be because of my choices.
Main "canon":
DA: O - male dwarf noble warrior - romanced Zev - Alistair is king with Anora; sided with mages, didn't destroy the ashes, Harrowmont on the throne, brokered peace for the werewolves and elves, and Alistair did the ritual with Morrigan
DA 2 - male mage Hawke - romanced Anders - sided with the mages, defended Isabela from the Arishok, and......(were there other major decisions....?)
DA: I - male qunari warrior - romanced Dorian - allied with the mages and Wardens, Hawke sacrificed, and Morrigan drank from the well
Alternate "canon":
DA: O - female dwarf commoner rogue - romanced Leliana - Anora rules alone; sided with the templars, destroyed the ashes, Bhelen on throne, sided with the werewolves, and no one did the ritual
DA 2 - female rogue Hawke - romanced Isabela - sided with the templars, defended Isabela from the Arishok
DA: I - female dwarf rogue - romanced Blackwall - allied with the templars, exiled the Wardens, Stroud sacrificed, and Inquisitor drank from the well
And, I've done a few other playthroughs for all of the games, as well. I just don't import them into the next game.
Oh, and communism is a red herring in all of my playthroughs as well!