I don't know much about Race Point, since I work at one of the other beaches. I haven't heard of any tire width rules, was it to skinny or wide?
I know that we have a rim height requirement, and that all tires must be the same size, includeing the spare. I know we don't fail anyone for inspections because they have skinny tires.
As for the CCCT, I don't beleive that you are allowed to transport any dangerous materials through it, you would need to use the bridges. Its mainly a safety reason, as you might know, but we don't want to take any chances in having our passageway blocked. But of course, you would need a permit first before you were allowed access to the tunnel, and as my understanding goes, I believe only residents are allowed permits.