I have done all three routes but not with a trailer - 1.) I-80 to I-15 to LV, 2.) I-70 to I-15 to LV and 3.) I-57 to I-44 to I-40 to SR93 (I don't know 96) to LV. All routes have altitude especially routes 1 and 2. The lowest altitude route is the southern I-40 route but it is longer and does have altitude at Flagstaff, AZ at about 7,200 ft but not for very long distances. However, with proper hydration (drink plenty of water) altitude sickness can be avoided. To completely avoid altitudes, get down to I-10 then go north but THAT will be a long trip.
A funny thing about altitude sickness, unless you have a definite physical problem that is sensitive to it, it may or may not occur again. I have had mild bouts of it only twice in my life when I was younger. I have since been higher and the same altitudes with no problems dozens of times. I hope this was your case and you should have better luck next time. I have learned to drink plenty of water and haven't had it since and can go to over 10,000 with no affect.
Good luck with your trip.
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