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I'm not sure if my 2 Tesla's can display in "% of SOC". I only see "miles". Guessing the % based on the nominal max charge is not simple because it depends on the temperature and the age of the battery.
Only 200 mile ? Usually you don't charge to 100% and you don't empty to 0%, so the real range is 90% to 20% or 180 mile to 40 mile. Without superchargers, you can only make 70 mile trip. With traffic jams and A/C this car won't make it across the Los Angeles Metro.
Same thing happened to my Model S last Tuesday in Oakland, CA . The car was parked in front of a restaurant on a fairly busy street. They cracked a hole on the quarter window, passenger side. Got a quote from Tesla service for about 1,300 bucks. Out of pocket cost is $150 deductible (AAA insurance).
The Model 3 LR should be able to do that trip without any problems. Flagstaff to Grand Canyon and on to Page is about 210 miles, within the 310 miles range of the M3. 120kW superchargers are available at Flagstaff and Page.