As stated in your original post: The blade only raises about 5 1/2 inches off the ground, but can be manually (pulling the blade up by hand) raised by more than 13-15 inches.
The above problem needs to be addressed first.. If your 3 pt. is truly all the way up, then you cannot manually lift it any farther. I would remove the blade from the tractor. Put the tractor on a hard level surface. Then, push the 3 pt control lever all the way forward and leave it there. Once the lower lift arms have bottomed out, the center of the lift pin holes should be approximately 5" off the the ground. If the arms are touching the ground, then you need to change the mechanical relationship between the lower lift arms and the rock shaft (I think that is what it is called) to obtain the 5" distance.
Once the 5" distance is obtained, then start the tractor and pull back on the 3 pt control lever and leave it there. Once the 3 pt is fully in the raised position, the lever will automatically return to the neutral position. Then measure from the ground to the center of the lift pin holes. You should find that they are around 22 1/2" and you should not be able to manually lift them any farther.
Once this relationship is established, then put the blade back on tractor and try it.
Good luck.