I tend to agree with Paul. From the sounds of things, you have tried most of what we can suggest.
When the tractor is bogging down, pick up the mower and see if you can charge ahead in 8th That alone in the field should take just about all the engine can give. If it will do it cold, but not hot then it is the tractor. If the tractor is OK, about the only other thing is the mower. If it is getting hot, something on it should really be HOT. Like if you spit on it, it sizzles.
With my 185, I had no expectations when I bought it. If I got it into grass that stalled it or bogged it down, I just went for a lower gear, and figured that was it.
I know the shorter you try to cut the grass, the more power it takes. With the bush hog I'd settle for 6-8" - anything shorter and the mower frame would dig in in too many places. But it took a bunch more horses to try to mow 3-4". I would imagine you are cutting pretty short, if it is lawn. As Paul suggests, pick it up a bit - or a lot - and see what happens.
I was always more impressed by what the tractor would do, than with what it wouldn't do. I had filled rear tires, dualies, and additional 280 lbs of wheel weights, the front loader, and a 200 lb homemade ROPS cage on mine. I don't believe it would even run in 8th gear. It would still run the bush hog in 4th, up hill. It took really heavy stuff to get me down to 1st.