Time will get rid of that. Lots of time.
Here's what I do for sweet, fizzy cider.
Ferment 2 gallons of cider. Let it sit for a month. (Pectic enzyme, nutrient before fermenting.)
Add pectic enzyme and campden to a 3rd gallon and let it sit for 2 days. Carefully combine the two. You don't want to introduce any more oxygen than necessary.
At this point, I combine them in a keg and carbonate.
To bottle carb, combine them into your bottling bucket with any additional priming sugar (I would be tempted to not add sugar and just rely on the sugar in the fresh juice to carb. It will be a little less sweet this way, though.)
Bottle in glass EXCEPT for one plastic bottle. Monitor that bottle carefully. The second it is firm (rock hard), you have to pasteurize or refrigerate. Pasteurization is a better choice. If you don't, you'll have explosions. DO NOT SKIP THIS STEP.