If it's where I think it is, you can go till you hit the locked grate.
I like to Cave Dive in Peacock, it is an easy cave.
Little River is the one that will get you bent if you are not careful. I used to dump ALL my air from my bladder before I would ascend. If it is pumping and you are the slightest positive, the current will blow you out like a Ping-Pong ball. I would bond up 5 feet and stop for 15 seconds, rinse, lather, repeat till my deco stop. Let the current work for me rather than against me. At Little River, most of the dive is at over 90 feet depth IIRC, it is almost always going to be a deco dive.
I haven't been Cave Diving in years and my old Instructor is pushing Sidemount hard now. I told him anywhere that tight, I did not need to dive.
And yes, I am IANTD Cave Certified.