CC, the GM BFB flour is fine and certain not the problem. I am currently using an antique KA K45 Mixer to make my NY dough. Your recipe looks sound. Your complaint about the KA not mixing well is a fairly common complaint but I can make 2 suggestions which might help.
-You might consider upping your hydration by 1-2% points for a slightly wetter dough or you can increase your oil to 2%. I would probably be more inclined to keep your hydration still and up your oil by 1% to a total of 2% and see if that helps.
-Also when my dough just seems to spin around and not mix there are 3 tricks that I use that can alleviate that.
1) increase the speed momentarily to 3 or 4 to see if it will catch. Once it catches, you can lower it back down to speed 1 or 2. I use speed 1 for the entire mix.
2) stop the machine, lift the head and place the dough ball dead center. Now lower the C - hook right onto the doughball burying it into the dough. Start the machine again.
3) perhaps the most important trick. When the dough is mixing, if it starts to climb at all, I will lift the head just a little as it is mixing to get gravity to coax the doughball back down. Occassionally, I even had the head lifted almost 100% up and let the dough ball brush the side of the bowl as it spins on the hook. I give it about 10 seconds or so and it usually is enough to work itself off the hook. As the dough is mixing, I have my hand on the mixer head and if you were watching me, my hand looks like it is bobbing up and down almost constantly. If not then my hand is resting on top of the mixer head. I almost get into a rhythm with the machine. Hard to describe, but I find that if I do this technique, it's not often that I have to stop the machine to adjust the doughball.
Now if the dough is pretty well mixed already and begins to ball up and stay off the hook, that maybe a good indication that your have sufficiently mixed the dough and no more mixing is required.
But it sounds like the mix problem is occuring at the beginning when you are just trying to incorporate your ingredients. If so, it may be that you should up your hydration by a few points, but I would try the oil first plus the 3 tricks I mentioned, then up the hydration if you are still having problems.