I do the island hopper to HNL then to IAH then to Tampa... frozen fish that is deep freeze for a few days will stay frozen until arrival in Tampa without extra ice or such, at most I'll do my frozen liquid thingy but mostly that is for our drinking. This is a 1 pm departure 3 am arrival in HNL, night time departure out of HNL, morning departure IAH to Tampa... That's a long journey without freezing the things during transport.

So going NJ to HNL to the outer islands should be a non issue.

From Tampa to IAH to HNL, I will store my cooler in a hotel freezer then take the next morning on the island hopper back to the islands. Not a problem that way either.

Remember, your frozen goods must be able to stay frozen for 72 hours... incase of baggage loss. If items are really completely frozen and packed in 5 day coolers they last no issue. I do this 8 trips a year minimum (so 16 times as frozen goes both ways) for the last 15 + years.

I will say buying items out of a grocery store freezer does not mean they are deeply frozen. I always try to get items and freeze them myself for two days ahead of time minimum to make sure they are completely frozen.

2nd day air??? Frozen??? I would not consider it personally. I think you are very safe without the dry ice and would just check it in. My 2 cents.