Foxhollow--If crowds bother you, I'm not sure you'll be real happy in any of the frontcountry (drive to) campgrounds in the Park. However, since I've never been one for anything other than backcountry camping, I'm not really the ideal source.
As for fishing alone, that's what I do 90 percent of the time. I don't really think much about proximity to roads but when getting into the backcountry I do leave an itinerary of precisely where I plan to be. Except for truly remote regions off trail, I don't know that there is anywhere in the Park I'd give a second thought to venturing on my own.
Of course I don't know your level of fitness, your woodscraft skills, and the like. But I certainly don't think you need to worry about fishing alone. Indeed, to me fly fishing is essentially a one-man sport.