Think of Mt. Whitney as the Mt. Baldy Ski Hut Trail of the Sierra. You will not want for company. I would not worry a bit about going by myself, especially on the way up when everyone is bunched together. The descent is a more dispersed.
I go solo all the time. I have made a bunch of rules for myself. I let loved ones know where I'm going and I do not deviate from my plan...even if something cool to do presents itself. You have to feel comfortable out by yourself.
You have got to pick your hiking partners wisely. If you are not compatible with them they do you no good. I only go out with people I can trust on serious trips. This is a serious trip for you. If you can't trust your partner to wait for you at intervals, you have a problem. Generally, when I'm out will someone who is slow I will wait at various spots because I do not want them to get too far behind. All this has to be established to your satisfaction before you head up the trail.
As for training reliable training partners...hook up with a meetup group or six. Between Mt. San Jacinto, SoCal Peakbaggers and OC Hiking Club, you should be able to put together a very good schedule over the next couple of months.
