The body might be warped due to previous owner's over-enthusiastic tightening of screws. My Concentrics were like that. I just put them in a padded vice and "unwarped" them. So consider that possibility before spending a bunch of money for someone else to do the same thing.
My concentrics, which were horrible when I bought the bike, now idle smoothly at RPM far lower than I actually set the idle speed ( I set 900 RPM). But I went through them completely, truing all surfaces, new jets/needles/viton float needle, etc.