To answer the question, it would be a very long day, and probably not an enjoyable one.
To address other topics here, I once (October 1994) got a speeding ticket in Grand Canyon National Park, on the north side, between the north rim and the Utah border. I remember it was rather expensive (well into triple digits in $$$, and nearly 30 years ago). So yes that can happen.
I have had more than my share of speeding tickets despite being a rather slow driver (compared to what I read here). I tend to drive closer to the speed limit, not only to avoid tickets but also for fuel economy.
Many of the speeding tickets occurred in NJ, in which (at least in the '90s, when all this occurred) each town had their own police force which I assume had to raise revenue. I got speeding tickets on I-195 around the Six Flags exit -- there were places along the side of the road where the cops would hide. I also got tickets in Tinton Township (near Red Bank in the eastern part of the state), Lambertville (right across the Delaware River from New Hope PA), Howell Township (right near eastern end of I-195), and Brigantine (town immediately north of Atlantic City) for one thing or another (not speeding).
Funny thing was, for all of those tickets, I had a PA plate since I lived there (therefore was out of state which must have lit up the (collective) cops' eyes). I paid all the tickets, and none of them ever showed up on my record. Hmmmm.
Later, in 2001, I got a ticket on I-66 in Virginia, right near the Vienna metro station. I had a VA plate then, and that one DID show up on my record.
Have not gotten one since (22 years and counting).