Since the new SDC policy rolled out, I've only dealt with a CO-marketed, UA/CO-operated ticket that I've modified. I worked entirely though the CO elite desk for the change, so I can't chime in with whether I could have used UA as well.

I haven't seen any mention of the UA SDC policy requiring the same inventory bucket, unlike CO's which does. Finding inventory in your original bucket may be tricky <24 hours from departure if you're traveling on the lower fare buckets.