Bill,
There is a Sleeve Hitch Adapter for the Cub Cadet rear lift. There are a couple of different styles, but they still do the same thing. But, you also have to have the rear lift installed also.
Here is a picture of one type of adapter, which is a reproduction of the original Brinley:
http://ccspecialties.org/hitchslotted.jpg
You also need a rear lift. If you look at this picture of the rear of my Dad's 149 (Wideframe series, same as your 1650). It has the rear lift on it (See the rockshaft just below the fenders, right below the seat). It also had the gearbox/mount for a tiller. If you look at the bottom of the tiller "hitch" you can see the ears of a bracket below the vertical pulley, and beside the horizontal pulley. This is the other half of the rear hitch. With his hitch, you remove the tiller gearbox and reinstall that bracket, that is where the "U" shaped adapter connects, and the round bar is inserted into the hole in the upper rockshaft, and that is what makes the rear lift work with a sleeve hitch piece of equipment.
Here is a link to just the bottom "U" bracket that is the bottom of the hitch...
http://ccspecialties.org/pics/3ptbracketlarge.jpg
If you look at the 3 holes in the wide part of the plate, they bolt onto the same 3 bolts as the "trailer hitch" is normally installed. (The bottom 3 holes in the transmission.
Your Last question..... yes it is more than strong enough to handle ground engaging work. We plowed a 100' x 100' Garden every year, for 20 years with the tractor in the picture. That was with the weight of the tractor, chains on the tires, my 250lb Dad in the seat, and my 200lb self standing on the plow as "live ballast". I plowed my garden with my 1450, with my 350lb self in the seat and my 150lb son on the plow and chains on the tires, In one pass I hooked a tree root (this was virgin ground) and running the tractor WOT I killed the engine, and a later pass, hooked a different tree root and pulled the front wheels off the ground about a 12-18" before I could back off the hydro lever... none of the plow or tractor part "moved".... they are very strong. The hydro rear is very similar in design and strength to the rear in a Cub Tractor, and the Cub Lowboy, on the gear drive cubs, it is the exact same transmission!!!