Phoenix isn't a good idea at any time.
Your route is fine as the "fastest"... I'd probably take the 215 where it splits off of the 15 in the Cajon pass since it is a little closer to scenic and rejoins the 15 after shaving a couple miles off the route to San Diego, but that's a detail.
What sort of side trips do you want? Mountains? More desert-ish places?
On the southern side you can loop off the 15 at the SR169 in Nevada and go through Fire Valley state park on the SR167... ending up roughly in Henderson (a suburb of Vegas really). From there you can meet up with US95 and go into California through Searchlight, meeting up with interstate 40, which you would follow west back towards the 15. If you take National Trails Hwy off that you can even stop in Bagdad, or better yet take Amboy road down to Joshua Tree, which is a beautiful area. If you do that, you can meet back up with the 10 and take that west to the 15 to rejoin your initial route. Or better yet take the 86 through Mecca to the 78, go through Julian, and meet back up with the 15 in Escondido (in San Diego County).
If that's too much (or you want more mountains) you can keep going on the 15 to Barstow then take the 247 to the 38 to Big Bear... then follow the 18 to the 330... there is some breathtaking scenery through there and AFAIK all the roads are reopened after the fires in '03... you'll meet up with the 215, take it south to the 15, and be on your way.
If you want to be more coastal and ride one of the best known motorcycling roads in the area, take the 215 to the 74 west (better known as Ortega Highway), and ride it to i5... traffic will be a little worse on the 5 but you'll have some ocean views as you cruise down the coast.
I could go on...
Ride it like you think owning it matters.