I run a JD HX 10' on a 50 pto hp JD 4520. The hardest part is starting the mower. With electronic engagement, the pto starts so abruptly, it will kill the tractor unless I have around 2000-2200 rpm. A 15' would be much worse. In mowing heavy grass, it will bog down the engine but usually I need to slow down more to get a better cut rather from not enough power, but I think I am on the edge of running a 10' mower with that tractor. On a hot day, A/C on and mowing heavy grass, the water temp is near the upper limits of normal. I have to keep the radiator clean especially when mowing with the wind to keep the engine cool enough. Heavy grass is harder to mow than 1" diameter, shrubs and brush or small trees.
I also have a JD HX 15' on a 125 hp Case-IH 125. That tractor has no issues. It has electronic pto but with soft start and engages the mower easily. My 15' batwing manual states minimum pto hp is 55 and I think that is on the very edge as well. I have not tried it, but I am fairly sure my 4520 could not start the 15' batwing without extreme effort.
You would have 5' more mower and 12 more hp than my 4520. Overall, I think you tractor is over matched with a 15' batwing. I think you need to be in the 75 pto hp range to get best use. Before you buy, I would definitely put your tractor on the mower and try it in some moderate to tough conditions.