Stopped for speeding, ticket for something else

Hi All,
I am seeking your feedback on my situation, I have been stopped on the NJ Turnpike back in December for alleged speeding. It was 5:30PM on a Tuesday night and evening rush our traffic was usual, not bumper to bumper and moving with a good pace. Around exit 9, on a portion of the car lanes an unmarked state trooper car was on the solder, parallel to the road, with driver door cracked open. I was traveling in the inner lane, with cars ahead of my in the middle and right lanes. Everybody slowed down a bit, but he came after us and pulled me over. I have a clean driving record, no tickets in the last 24 months, no speeding ticket ever and I am 41.
He informed me that I was speeding, going 84 in the 65 zone and that he used a laser to measure me. I said that is not possible and showed him my GPS which showed a much lower maximum speed, I think 76. He observed that I also have a radar detector and asked if was good for laser and signalled anything. I said yes, and that it picked up no signal. He went back to his car and then issued me a "Failure to keep to the right" NJ 39:4-88 as he put it because of my "clean driving record". This is still a 2 point ticket and $150.

My question(s) to you:
- does an officer have this kind of leeway? is like catching someone with murder but citing petty theft.
- if I decide to fight this, which offense will I be charged with and I have to contest in court?
- if I have to contest the cited violation ie. NJ 39:4-88, the fact the trooper had a chance to observe my traffic pattern for about 300-400 yards would make a good argument. He was on the downhill side of a small hill

I think if everyone traveling longer in the left lane for more than 3-400 yards on the NJ Turnpike would get a fine, we could pay back the national debt in no time...
Your feedback is much appreciated.
Lleo19