I was just at Beasley. Went in a 73 Land Rover with decade old mud tires, 80hp, and a rear locker.
There is a phone number on the website. Its an automated number so feel free to call it whenever you want. I checked and they close it often due to rain. Rightfully so as that place has some pretty severe elevation changes. If its dry it isn't a problem but once it gets wet, its pretty much impossible. Because of this, they close it often. Tried going three times this year, 2 weeks ago was the first chance I could make it.
I actually went one time when it was wet. Oh jeez that was a cluster.
Judging from the moisture here in Kennesaw, definitely keep checking up on its availability. Making a 45 second phone call from your comfortable home is easier than driving up there to find a locked gate.
Overall, I had a ton of fun but yeah, 93B is a pain for anything unlocked and not on 35s. Heck the ATV couldn't make it up there on its own. I ended up having to ride the winch cable up it. Avoid that trail and you should be fine.