how did you add your priming sugar? sounds like it wasn't mixed well.
Easiest way is to dissolve your sugar by boiling in a small amount of water, add that to the bottling bucket, and rack your beer onto it. You can swirl (gently) for a bit to ensure it's mixed in, but I never did, and never had issues with inconsistent carbonation.
Can't comment on the carb tabs. But I would suggest trying the above before you go the carb tab route...table sugar is really cheap.