Above logic seems good to me.

And since your company is less inclined to like anyone flying UA but may not mind CO, you could still burn the miles you've earned on later flights with its partners such as the one I consider to be one of the world's best: Singapore Airlines?

And since Singapore Airlines IS aligned with UA and CO, this actually makes me suggest that the OP lean toward UA as well. AA might be good and all, but their other partners are no where as good in my opinion.

What I don't like is when companies try to tell ya how or whom to fly.

MM