The "traditional" way to run the Rubicon is from Loon Lake to Tahoe but you can run it both ways. I will be on the AJC trip that weekend, which is typically a very crowded mess. Since you will be going in on Sunday, I suggest you start on the Loon Lake side since many will be exiting the Tahoe side. You will run into rigs exiting to Loon (most AJC participants do) but it shouldn't be too bad. If it were me, I would plan to try and get to Buck Island Lake and camp there Sunday night. Hard to say how long it will take you since I don't know what the traffic will be like or how fast you go but a good guess would be 3-4 hours, assuming nothing breaks. From there, pencil in another 3-4 hours to the Springs (super slow driving) and enjoy the scenery. Camp in the Springs Monday night, and then exit to Tahoe side Tuesday AM, I have made that trip as fast as 2 hours, but factor in "stop and smell the roses" time.
You can leave the truck/trailer at the "Chalet" which is a big dirt parking lot just before the Loon Lake dam. The problem you might run into is the lot might be full if you come in early Sunday, but as the day progresses, the lot empties out fairly quickly. Of course, you then have to circle back down Hwy 50 to get the trailer (expect another couple of hours).
feel free to PM me if you have any other questions, I am happy to share my experiences but certainly don't have all the answers...