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Hi I'm Kevin if there was a ring issue you would have smoke under load .how much oil have you used in the 1000 miles?
When you say rebuilt is this the full engine of top half?
Ok when engine is rebuild it will have a running in period where oil consumption is slightly higher .if it isn't leaking there will be some smoke at some point in drive cycle .its easier if you get someone to follow car whilst it's driving to see smoke I would give it another 1000 miles and see if it improves is not like you say it could be a bad ring this would show up as smoking under load
Give it the miles first you have nothing to loose it may wear itself in if not the rings are where I would be looking