"What is this nonsense," you say, "Zeppelins are aircraft, it would be silly for them to follow predictable trade routes, especially in the pirate-infested airspace of the former USA!" Well, that's partially true. Zeppelins are aircraft, but they're aircraft that historically had a 3,000 foot pressure altitude. While they had the lifting power to go well above that altitude the pressure differential between their gas cells and the thin outside air strained the valves and brought the cells dangerously close to rupture. The USS Macon was damaged flying over Arizona this way. Using historical zeppelin technology, flying coast to coast in a zeppelin would be too dangerous to be routine.
See? The whole interior of North America is basically a zeppelin-free zone.
But this is alternate history! Historical zeppelins had gas bags made out of doped cattle intestine, were practically hand-made in tiny numbers and had an alarming tendency to explode. CS zeppelins are obviously a finer breed, mass produced, reliable and made of tougher stuff.
In our timeline, polychloroprine synthetic rubbers were first synthesized in 1930, and these are used in high-altitude weather balloons. CS zeppelin gas bags could reasonably be made out of something similar and their pressure altitudes would therefore be much greater, perhaps on the order of 6,ooo-8,000 feet or roughly the same as the Zeppelin NT.
... which still doesn't leave them much clearance when it comes to flying Allison engines made in the ISA to Hughes Aviation factories in the Nation of Hollywood. Looking at that map, I see four options for getting coast to coast in a zep.
1) Swing WAY north over the uninhabited portions of Pacifica, and cross the Rockies over their various low points. Try to avoid attention from warring Russians and grumpy Lakota. This route is good if you have business in Pacifica and the ISA.
2) Go south of the Sierra Nevadas then cut north through Deseret and northwest Free Colorado until you pop out in the People's Collective. Free Colorado is full of pirates, but most of the big population centers are on the opposite side of the Rockies from you, and will thus have difficulty jumping you. This route is direct and you're not flying over anyone likely to charge tariffs, but it's crawling with pirates. The altitude floor is also quite high, so you'll likely only see zeps with the very best gas bags or the most reckless captains along this route. Tramp freighters and priority high-speed shipping would use this route.
3) Straddle the Mexico border along Texas and Arixio. Expect to pay tariffs cross the Texas border. This route is direct and safeish, assuming there's not a shooting war going on along any of those borders that particular day. Probably good for those with business in Dixie or Louisiana.
4) Go through southern Mexico. Expect to pay tariffs to the Mexican government, and it's extremely roundabout, but probably the safest option.