Rule #1: You may think you know all the dangers to watch for, but Mother Nature is way more creative than you and can smack you with ways you haven't even thought of.
The remote for the winch seems like a good in concept, but (IMHO) I don't see the extra advantage being greater than the added expense and added complexity (reduced reliability?). The argument for one is it saves you an extra trip walking if the log hangs up on something, but chance are you didn't walk to the log with a peavey/pike or snatch block and anchor chain so what are you going do (i.e. you're making an extra trip anyways).
Granted, if you're choker chain slips off (there a bit of a learning curve if you're using an "open face" grab hook instead of a ring on your chokers), then maybe a remote could be handy. But it seems like a remote creates the opportunity / risk of being too close to a moving log (and its branches). (See Rule #1)
Never heard of the log hitting stump going end over end log danger. Only the: if log but hits stump, tractor can quickly wheelie. There is a similar real danger of using winch to pull on a tree that is hung up on another tree. Winches are the safe way to do this, but their power can lead to unexpected results (i.e. instead of the butt sliding toward the winch as expected, the weight of the tree (or a root/rock, etc) holds the butt into the ground and it becomes the fulcrum for the whole tree to suddenly raises straight up into the air and then the top of the tree falls towards the winch).
I agree with the commenter that says watch the tractor end of the cable and glance at the log end. You'll be able to see if the cable stops quicker and you won't be burning up the winch's clutch as much. If the cable is moving, chances are everything is good at the other end (this also allows you to see that the logs are coming to the tractor and not the tractor going to the logs. (Stand to the side of tractor when operating so you don't get run over by the tire in this case.)
Make your tractor as heavy as possible. Load the tires.
Use caution if not pulling straight on. Most winches could probably overturn your tractor if pulling from an angle and log gets hung up. (Again, another reason to be watching tractor end)
I think my tractor is a bit heavier than the one you're looking at (but maybe not if you have cab). I have a 6500lb rated winch (cranked up a bit more), it does 98% of what I need it to do, but I wish it was next size bigger.