I think the
L3800 has a lift capacity of 1400 pounds 24 inches behind the arms. That is going to really test out your hitch with a mower that heavy. Like you I LOVE a stout mower, gives confidence and its fun but I've had a too heavy of mower on a tractor before and its pretty miserable to operate with it's weight back there wagging the tractor.
Does the 3800 have a aluminum rear axle on it? If it does I would go with the 2060 for sure. The 2060 will cut down any wild rose in Kentucky and any vine also. If you do decide to get the heavier mower you will for sure HAVE to have front weights or a loader on when your mowing,if you decide to use the top link and lift up the mower with the hitch. You could leave off the top link and use the mower in a "simi-mount" configuration where its always riding on the back wheel.
On those two mower I notice that the 2760 is listed at 955 pounds and the 2060 at 590 pounds. Thats a big differnce and the lighter one would be much more controllable on your tractor. Here is another benifit of the 2060, it has very high blade tip speed of 16,300 feet per minute. The heavier duty 2760 has a slower 12,380 feet per minute. The higher tip speed of the lighter mower should (in theory) give a nicer and cleaner cut if that is important to you.
With your tractor I would go with the lighter 2060 if it was me. I think you'll find it is a plenty tough little mower for what you want it to do and will leave a finer cut and be easier on you and your tractor's hitch. That said, if your going to mow with a loader on, if you have fluid in the tires, if your rear transaxle is cast iron,if you not concerned with a "lawnmower" quality of cut and your going to mow over some bigger saplings then the heavier 2760 is the mower for you.