Excellent back road from Buckeye to Salome with WAYYY less traffic than US 93.
Country store off route 1.5 miles SOUTH of junction of Courthouse and Harq Valley Rds.
BTW - Salome Rd is unpaved and very sandy on the diagonal between Courthouse and Harq Valley Rds.
But if you follow the highlighted routes - it is paved all the way.

Also, if you use Calif Hwy 62 - you may be able to beg water at Iron Mountain.
You can't count on it, but I would think they would be hard pressed not to give you any water.
When you get to Twentynine Palms you can ride thru Joshua Tree NP to avoid busy highways.
Then follow local roads thru Palm Springs. Get a local to show you the best roads to Beaumont.
West of Beaumont consider San Timoteo Canyon Rd.