Depending on weather and the snow pack, May is questionable, June can usually be safe, and July is better - weather wise.
Now I know you said want to avoid the summer crowd - here's a few pointers:
1 - Holiday weekends (memorial day, july 4th, etc) and Jeeper's Jam weekends / weeks are nuts... I avoid them if possible, or just plan on lots of traffic and frequent pit-stops. Jeepers Jam weeks the trail is actually closed if you haven't paid them for a spot on the trail ride - they "own" it during that time.
2 - The Rubicon is not a trail to take alone. Things break and people get stranded every day. The good thing about crowds is 99% of the people on the trail will stop, help you fix, give you spare parts, use their on-board welder, or tow you to the exits or the springs for more knarly repair needs. At worst care, you can usually catch a ride out and back to your rig with the parts you need.
3 - In addition, injuries from roll-overs and other accidents (snake bites etc) are so much more dangerous as the only way to get to a hospital is to exit on the Tahoe side and Jam at least a 1/2 Hour either way along the windy lakeside highway / road, or exit the loon lake side and take a hour to get down the mountain, and then go back into placerville, ca (another 1/2 hour at best). Alternatively most people who run the Rubicon have HAM radios and program them to the local repeaters to call for emergency airlift services (ambulances are not getting to you...) This (without some very good and reasonable airlift insurance policies) could bankrupt a normal person in expenses, but broke or dead - I chose broke... Remember - this doesn't count the time you need to actually get to a exit on the trail, or a spot a helicopter can reach you.
4 - Sometimes traffic Jams occur (we call them trail-tampons
), and they provide a good chance to stop and really see the beauty of the mountains you're in.
Point is - I say none of this to deter you from running the trail - I love it. I also like to not have a million people on it with me as it's just not fun if it's too bad... I also, however, do not run the trail on the times of year that basically no-one else is on it, even though I always wheel it with my Uncle in his
CJ5 too. It's a fine line...
I'm going to make a Rubicon Trail ride post soon and will detail more about the what to expect, bring, and best anticipated time to run it. Hopefully I can get a few others to come out too.
Let me know if you have any other questions