My concern is that I've read on long weekends you can wait hours for a SC. I drove back on July 4th weekend and it took me 7.5 hrs to get back. The traffic in baker alone was about 45 mins, so I can only imagine what the SCs looked like.
i've done the trip from LA to vegas about 5 times i think since getting my model 3 (exact same car you're asking about, 2018 LR RWD), and i can't imagine there's any chance you can make it without stopping unless you enjoy pissing people off and/or potentially being run off the road a few times. you'd literally have to average 55mph (maybe 60) to do that trip without stopping. of course, if you're talking about a long weekend traffic-wise where you're going to be averaging 40mph the entire trip, then MAYBE you could make it without stopping.
that being said, you're worrying way too much about how long you'd have to wait for a SC. you've got four potential stops in the desert (barstow, yermo, baker and primm) to pick from, and baker is HUGE (40 stalls), yermo is no slouch either at 18 stalls.
it's highly unlikely you'd have to wait for hours at either location, IMO. i've never even had to wait at yermo (although one time we did get the last stall available and there was one car waiting when we came out). i've never stopped at baker (we always prefer eddie world based on amenities), but i check the map every time we go and it's never more than half to 3/4 full. there are always at least 10 or so spots open, at least on the times i've done this drive.
likeliest scenario: you pull into any of the four SC (checking the map along the way for availability), plug in, use the restroom, get back in your car and make it with plenty of miles to spare...along with being able to do 80+ the entire way if traffic allows. a single stop for a few dollars and not having to worry about it vs unnecessarily trying to save just those few dollars in electricity and potentially getting stranded in the middle of the desert is a no brainer, IMO.
edit: just put my home here in lake elsinore into a better route planner and set las vegas as the destination (no address, just the center of the city). from HERE (so i'm about 80 or so miles east of LA proper, which means it'd be even worse for you depending where you're coming from), and then blocked out every charger along the way. it tells me i can make it without stopping if i only average 56mph the entire way. no thanks.