Gena, glad ya came back! Yea I'd be afraid you would tear up jack in the trans axle before to long. If your willing to try it, just be aware of the precautions.
The sleeve hitches that Craftsman indicates are only for Craftsman, I 've seen them on different LT's, oops, I mean GT's and they can be made to work. If you mod your attachment of it, and you do try to use the cultivator, just don't try to dig in with it too much, or the trans axle could be your first heavy duty repair job. If you do use it, just don't pressure it. You might get away with it that way. The other consideration in the equation, is your drive belt will also be placed under more pressure from the drag and could need replacement sooner than normal. But, again, if you go easy, you could possibly do the chore you are wanting to do.
Here is what I think you have and here is a Murray GT, I just finished doing a refurbish job and it is sold, to be picked up by the weekend.
Notice how the tires and frame of the red LT are so much lighter weight than the "Green Machine" GT, which has much bigger wheel/tire on it. Also notice the back slope of the GT on the frame body at the back, and the straight up and down back end of the LT. Just some considerations for you to look over.
Also, the red example I had is a hydro automatic, so if you happen to have a hydro, don't even think about it!:Stop: