All casting instructors tell their new students not to use their wrist because otherwize the students drive the line into the ground behind them, then pile the line up like spaghetti in front of them.
The fact that you are hitting your rod is actually a good sign that you are "getting it". Your tracking (keeping the rod tip in the same plane -ie.in a strailght line forwards and backwards) is excellent. You are also achieving very good "SLP" (Straight Line Path of the rod tip in the horizontal position).
That means that you are applying enough force to the rod handle to bend the rod so the tip does not form a circle when you rotate it, but bends enough so that, during the power stroke, it would draw very close to a straight line when going above your head. That is excellent progress.
Now all you need do is extend the length of the casting stroke forward, and snap your wrist just as you run out of arm length.
Read this and look at the animations on each one:
Virtual Fly Casting - Instruction - The 5 Essentials
The line hitting the tip is a very good sign. Just think how tight your loops have to be to do that.
PS: I am surprised that Ard hasn't jumped in on this one. Ard uses ONLY his wrist when casting and is a very accomplished fly fisherman. I also use primarily ONLY my wrist when getting line out false casting. But we know how to control loop size and line direction with the stop and release timing.
You will too if you keep at it.
PS: I think I have some broken out stills of a video I took which will give your a better idea of SLP. But I'm rigging up my 9 and 12wts in a couple minutes. A buddy wants to go out for blackfin tuna in a couple hours. I think there will be some billfish around if we can find the tuna. Hence the 12 wt.