My 2 cents worth:
I also tow a Puma but it is the 25RBSC, twin axle about 5600 lbs unloaded. it is similar but not the same as the one in the photo.
My truck is a 2002 SB 4 door 2500hd 6.0 but the 4 speed 4L80E transmission. I stay in tow haul mode when pulling and honestly will say it struggles to go up a moderate hill at 60-65 mph, but I will also admit that I dont romp down on the engine either.....and I do think it is part of my problem because more than once I have read here and elsewhere that folks rev that 6.0 up while towing and they also say dont be afraid to do it.
It is my understanding that the 6.0 builds most of its torque at around 4000 rpms...which is probably part of my problem because I try to keep it at 3000 or less when accelerating.
I have pulled the same camper with a straight drive 7.3 F-350 turbo diesel and of course it was a difference of night and day but diesels build power in a whole different way. Personally I dont think any gas engine is going to go up a hill passing anything other than a turtle without a whole lot of rpms thrown at it ( Now I say that without ever being behind the wheel of the bigger block Chevys and Fords, so as I say its only two cents worth of opinion) but I do think if we all take that over-rated factory tow ratings from ALL manufactures and reduce that maximum tow rating by 50%, and stay within a 50% reduction then we we will have a decent towing gasser vehicle.
In all honesty I think Im rated for 10,000 lbs and I would really hate to try to run at highway speeds with 10000 lbs at 65 and jamb on the brakes even with the brake controller at it highest setting. I think 10000 lbs going up a moderate hill...say a 1/2-1 mile long would be tough to do without losing speed.
However, the OP's trailer with a zero turn in it should pull without any trouble at all...I do think there is a problem somewhere...I have a drive on trailer but its a single axle equipment type and the other week I had a zero turn on it and it towed it with no problem at all...Im thinking i was probably around 2000-2500 lbs and didnt really feel it back there