That sounds tight....if you are at the start of the parade, I would think by 4:20/4:30 would be the ending (i have never timed it..maybe someone out there has?) You need enough time to get out of the park, then the bus to the POLY..They normally say 1 hour but just to be safe I'd try to get a 6:00 adr.
We saw the JJP last year & then had a 6pm Boma ressie which worked out great. Also consider that AKL is 5 minutes away,,the poly is going to be farther.