Update:
I believe my problem turned out to be a dirty/clogged carburetor. I checked the spark and it seemed to be nice and strong. I tried spraying some carburetor cleaner around the gaskets while running to see if anything changed, but it didn't. I also tried turning the main jet screw to see if that had any noticeable effect, but it didn't.
Since a carb kit was not very expensive, I figured I would go ahead and give that a try. I have never done a carb rebuild before, so I was a little nervous. But like I mentioned in my original post, I have a manual and there are some online videos showing how to do it.
So I purchased a carb rebuild kit, removed the carb, took it apart, soaked it in a can of carb/parts cleaner, blew out all of the passages with spray carb cleaner and then with compressed air, reassembled the carb, and then installed it back on the tractor.
The tractor fired right up (which it was doing before already), but when I sat in the seat and engaged the PTO for the bush hog it spun right up without a single hesitation or problem. I was able to go right out and do my bush hogging without holding the choke out or anything. The tractor ran very smooth and had plenty of power and didn't try to go dead at all.
I want to thank everybody for their advice and suggestions. I really appreciate it!!
I also wanted to make sure I posted a resolution to my problem to keep the thread "complete". Many times I have read threads where a poster describes a problem, gets advice on how to diagnose/fix the problem, but then never posts back to disclose how their situation ultimately turned out.
Anyway, thanks again to all!!