You didn't say what type of battery your car has, but it's only 168 miles with a ~500 ft. elevation gain and it's unlikely that the weather will be bad in that area so you should be fine. I'd want to charge to 250 rated miles at least just to be safe. Then slow down if necessary. If you have 300 rated miles, you shouldn't have to monitor your speed or arrival SOC at all. There are some decent food options near the Indio supercharger so you should have stuff to do if you decide to do a long charge there. I liked Your Pie Pizza.
You're right about there not being much along that route. There is a gas station/convenience store at Chiriaco Summit and a very small gas station/store at Vidal Junction (or at least there was last time I went through there a few years ago), but that's it.
Another option would be to go via the superchargers at 29 Palms and Primm. It's not as long as the route through Indio and Needles, but you could get caught in the LA/Vegas traffic when you join I-15 50 miles south of Vegas. If you do go that route, be sure to check the road conditions through Mojave National Preserve. Those are some very desolate roads and I know there have been some heavy rains in the past year and there could be some washouts. Amboy is a pretty cool Route 66 ghost town and the depot at Kelso is also worth a look if you do take this route.
Honestly though, I highly doubt either of these alternatives will be faster than just sitting in the traffic on I-15. So if you are up for the adventure and want to check out some different roads, go for it. But if your objective is to get to Vegas as fast as possible, I would just map it out on Google Maps right before you leave (point to point only as drive times don't include traffic when using multiple waypoints) and take whichever looks faster. The Nav will also give you a 2nd opinion, but I would always use Google Maps as a primary source when planning out a long drive with potential for traffic.