Your Puma has a dry weight of 8663 and will probably weigh at least 9,000 pounds with anything in it. That's a tongue weight of over 1100 pounds, or way too much weight for you to be dragging the trailer backwards with only the tongue jack wheels to handle that weight.
So your idea of adding a receiver hitch to the rear end of the trailer won't work as you expect it to work. You can add a fabricated receiver to the frame of the rear of the TT to be used for dragging another trailer behind the TT, but probably not for dragging the TT backwards.
So on to Plan B. Either one of Old-Biscuit's ideas will work to do what you want done.
There are several brands of tongue dolly trailer movers available, both non-powered that requires lots of muscle to move the trailer, as well as powered units that will take most of the work out of the task. And there are several brands of front end receiver hitches available. The only problem with using a front hitch to move the trailer is that same 1100 pounds of tongue tongue weight that would probably overload the front suspension or axle of the tow vehicle.
Here's a powered tongue dolly that uses an 18- or 20-volt battery-powered drill motor for the power source. If you don't already have a good battery-powered drill, you need one for other chores besides moving the trailer.
Plan C: Use a receiver hitch on the rear end of the trailer with the tow vehicle as the power source, but also use a manual tongue dolly to handle the tongue weight. Then two people could easily move the trailer, one to very slowly drive the tow vehicle, and the second to guide the tow dolly.
Any good welding shop can install a receiver hitch on the back of your trailer. But they would probably need to extend the frame of the trailer back closer to the rear bumper. That can get expensive. So it would probably cost you more to implement Plan C than Plan B.
Grumpy ole man with over 60 years towing experience. Now my heaviest trailer is a 7,000-pound enclosed cargo trailer, RV is a 5,600 pound Skyline Nomad Joey 196-S, and my tow vehicle is a 2019 F-150 Lariat 3.5L EcoBoost SuperCab with Max Tow (1,904 pounds payload capacity).