If you want to go that route, there is no problem with switchbacks. It is a bit easier to swing into the oncoming lane just slightly on one of the switchbacks, but the other lane is wide and plenty of view coming out so no worries about oncoming car. The switchbacks are also on the steepest part of the climb as they really clung it to the vertical side of the mountain in that section. I've done it plenty of times with a 30' TT and a 35' FW.
Don't plan on stopping at Ceasars Head while you have the trailer in tow. It's still doable, but made a lot harder by the entrance way they installed a number of years ago. Besides, Ceasars Head is only a few miles back up from the campground so easy to run back up.
Because of where you are going, if you have the truck, 276 is probably the easiest way to get there from the upstate.
