If you think an AI is hard, wait till you try retrieving a TI!
A dolly type cart is easier for retrieval, though maybe not in rough beach conditions. SunESailor's 'appel' cart was based on using a TI trailer cradle. I copied it and mounted it to a Rhino roof rack bar. You may be able to adapt an AI cradle. See viewtopic.php?f=73&t=35157
Could dragging the AI one handed be contributing to back problems? Adding an extra handle so you can use both arms evens up the pressure on your spine. In my experience it's the uneven twisting of the spine that causes problems. Lifting the AI while holding the cart is asking for problems. Try positioning the cart close by then lift the folded AI with both hands, standing 90 degrees to the hull. Once the balance point is reached then insert the cart.
Leaving the mast in will make it less of an effort turning the AI on its side and shouldn't cause any damage. I seem to remember Matt Miller recommending this a while ago.