Haven't been there since May, but I believe the part of 58 that is closed is actually the Business 58 out of Mojave that connects to the main Hwy 58 as it does not go through Mojave any longer.
To the OP, Hwy 58 out of Barstow turns into a two lane highway just a couple of miles off of I-10. It does turn into 4-lane about 10 miles further and then back into a 2-lane about 10 miles from Kramer Junction (intersects with Hwy 395) and stays 2-lane until Boron. It then is 4-lane all the way into Bakersfield. There is a small grade before Tehachapi and then a long downgrade down into the valley with grades of 6% or less.
Should not be any kind of a problem for you with the exception of the construction at the Sand Canyon overpass.
Hope this helps
Ron