The Jasper Trail heads into Grapevine, neither is what I would necessarily call challenging (especially for your rig...) although 4WD may be required in certain sections depending on conditions. There are a couple of rock-garden style sections off the side of the trail, all of them are in/out.
It's a fun, scenic route, lots to stop and explore but keep out of the no-trespassing marked sections. There are active, working gold mines in the area and they don't take kindly to strangers. Be sure to close the gate(s) behind you if they are closed when you get there.
If you're going out through Julian and down Banner Grade you can catch Rodriguez Canyon at Banner, follow it (and catch Jasper) over to the S2 and then head up to Pinyon Mt.
The Squeeze/Heart Attack Hill trail can be run in less than an hour. Once you pass the last little climb past HAH and hit Split Rock it's pretty much trail running that will give you a great appreciation for your suspension.
There's a couple of sweet camping spots right before, and just past, The Squeeze. Look off to the areas on the north (left) side of the trail in. You could also camp at Blair Valley, one of my favorite spots, and run Pinyon Mt in the morning.
If you're making a day of it you could easily run Rodriguez, head over to Squeeze/HAH and the head south through Canyon Sin Nombre and mosey over towards Dos Cabezas or go the other direction and take Fish Creek/Split Mt Road towards Ocotillo Wells. Lots of camping spots, there's a nice camp site at the north entrance to Fish Creek and then you could hit some of the in/out canyon trials south of Ocotillo Wells (some of those reach into the challenging territory)
Sounds like your Saturday will be more fun than mine