Two suggestions to help isolate your problems
1) Use carb tabs for a batch. You should have even carbonation, which then indicates poor distribution of priming sugar when you bulk prime. If you still have uneven carbonation then I would look at your capper.
2) Buy two cases of new bottles. Keep in a bucket of starsan and empty them right before you fill them. Fill them wet it's fine. If you still have sanitation issues, replace ALL of your plastic. If you don't, something in the way you are handling your bottles from cleaning to filling is the culprit.
If you have starsan, why are you oven-baking?
