There are 2 trips reports for Mono on paddling.net. Check them out at http://www.paddling.net/places/CA/ and page down to Mono Lake. Unfortunately, neither covers the rules for camping, which I hear is legal and also heard what you reported - that the islands are off limits during part of the year.
I haven't paddled there, but have visited. Water is very alkaline. When you get wet, it provides a feel on the skin much like when you get bleach on you. I'd want to bring a lot of rinse water to try to get that stuff of the boats before putting them on the car.