That beach looks like hard-pack to me. You should be flyin' on that stuff. I find just-above the waterline is the best packed sand, another few feet away from that, and you'd be in sand so-soft, it's hard to ride at-all. SE Florida.
Glad to hear shims did the trick. Wasn't some-sort of runout evident?
I haven't tried a fat-tired bike w/those size balloons. About 27 years ago, I bought a Klein Attitude w/full Shimano XT, top of the line then, but I replaced the XT brakes w/Scott-Pederson self-energizing brakes, which were a really-great product for the day. I raced that bike for a couple of years in NORBA events here in south Florida, and I took it to San Francisco/Marin Co. a couple times, when visiting family. The tires I liked best on it were Ritchey Kevlar bead folding tires, I got the biggest that would fit, they were 2.35" and were good for the day, especially if you let out a bit of air from road use pressure. I used to ride on the oceanfront through a city and county park to the jetty entrance at Port Everglades (Ft. Lauderdale) from my home a bit south, on the west side of the Intracoastal Waterway. The Klein was a bit over 23 lbs. and was an old-school ride, no front suspension, no rear suspension. Factory was an integrated handlebar/stem and a fat set of very-lightweight forks, but with large diameter tubing, they steered like a dream, and the frame was light but rigid, w/good response to your input. The year after it was purchased, Shimano released their first XTR gruppo, I brought my bike in when they got their first sets in, and had the XT transferred to a chro-moly frame, and the XTR installed. The XT was good, but the XTR was really-good. The shifting mechanism was much-better, and more gears too. I still have the bike, but I don't ride competitively any more, and have slowed-down, being close to age 70. I really enjoyed riding on the beach w/those tires, I imagine the wide wheels/tires of today allow an easy time of it, despite what I assume to be more rolling resistance.