I have a 3320 with a 447 backhoe. I do not use the "factory" described method to remove or install the hoe, I was never able to adjust the hooks to where it would work to remove or install the hoe every time. With my method the hoe is off or on in two minutes, every time. It is probably not as safe as the factory way.
To take the hoe off, try this. Engine running, off the seat. Make certain the rockshaft control lever is in the down position. Then to remove the hoe take the clips off the big pins that hold the hoe to the frame, level the bottom of the bucket, and place a cinder block on the ground under where the bucket will rest. Then lower the stabilizers until they both just take the load of the hoe. Step to the right side and ease the right stabilizer up or down ever so slightly till you can slip the big pin out. Once out go to the left side and do the same with the left stabilizer. Once both pins are out, ease both stabilizers up at the same time and this will lower the hoe so the bucket rests on the cinder block and the hoe on the ground. Once on the ground raise the stabilizers all the way up and turn the engine off, and then wiggle the boom lever and stabilizer lever just slightly to take the pressure off the hydraulics then disconnect the quick connects and connect the line for the 3-point hitch. Before starting the tractor make certain all the hoses are clear and firmly connected or not. Sit on the seat, start the tractor, make certain the hitch pins have cleared the hooks, then drive off. Two minutes, honest.
To install or remove the hitch arms takes a bit longer, but it is pretty straight forward. The only tip I can give you is to remove the lift links from the tractor hitch arms last when removing, and put them on first when installing. Use the lock pins too, it just holds everything up while you take off and put on everything else.
To put the hoe on, raise the hoe as high as it can go with the rockshaft, do not let the hydraulics go into relief, if it does, just back off a bit on the rockshaft lever. Turn the tractor off. At this point, DO NOT TOUCH ROCKSHAFT CONTROL LEVER. Disconnect the hitch hydraulic quick connect (one line) and connect the hoe hydraulics (two lines). The rockshaft will maintain the hoe in its position even when the line is disconnected. Off seat, start the tractor, and lower both stabilizers together just enough to take the load. Now you can lower the rockshaft control lever, the rockshaft will remain in the hoe hooks but will not be carrying the load. Step to the right side and ease the right stabilizer up or down ever so slightly till you can slip the big pin in. Once in go to the left side and do the same with the left stabilizer. Two minutes, honest. Oh, and don't forget to put the clips back in the big pins.
It takes some practice to be gentle with the stabilizers. Be easy, be careful. I hope I didn't leave anything out.