How much oil consumption are we talking about here? I know a couple guys running older 836 kits and they had 1-piece oil rings at 10.5:1 compression and the worst they show is a puff when you really get on the throttle. Cruising around and at lower R's there's no noticeable oil smoke.
Many of the stock Honda rings were one-piece and they were also fine. So, how much oil are you burning?
I haven't been following your previous threads, so if any of these have been addressed I apologize, but here are some possible issues. Did you check all your ring end-gaps (oil-ring included) and what were they? Are you certain the two compression rings are installed correctly? The middle ring (lower compression ring) acts as a scraper of sorts and if you put it in upside down it will burn amazing amounts of oil.
And lastly, have you contacted the place that sold you the kit to see if anyone else has had this problem? Perhaps there is a common remedy. I wouldn't be so quick to blame 1-piece oil rings for severe consumption on a new engine.