I know that I'm missing focus-my question is how to I get there so that I DO get focus, or just have a higher probability of getting focus on more of these shots? It's comforting to know you think I'm close on some of these-I feel like they're just so far away
C. Brian Kerr-just for you, I've attached one of my faves of her. The 'catch lights' from the snow are a bit annoying but I love it anyways
You are sooooo close on a number of these! This shot
Freeze Motion - Slow Lens and Flash Photography Forum is pretty good, but the depth of field is just a bit shallow to get full focus...a significantly slower shutter speed + second curtain flash, right on-camera, in the hotshoe, could be pretty good here...the ISO needs to be "high-ish", and the speed needs to be "slow", like 1/8 to 1/20 second or so.
Panning is a great way to convey movement, and one of the very few times where I will actually FAVOR shutter priority, Tv or Time value as Canon calls it, to keep the speed at the right level. You could try that approach, slow-speed panning with second-curtain synch.
The other DOF issue/tip is to shoot at right-angles to the dog, perhaps easier said than done, but maybe if you give the dog a triangle-shaped course, he'll tend to run in a line for one leg of it?
The other option is getting the ISO level UP, high...after work, this time of year, it gets dark pretty fast until July and August roll around. With a longer lens that tops out at f/5.6, at ISO 500 you8 mighty be as slow as 1/50 second in many yards...I was out today, and was getting f/5.6 at 1/50 in the shade here around 4:45 PM.
ISO at 800 is already too high-I get noise in her fur and it looks awful, and takes away from everything. Higher, and I might as well add another noise filter.

I stay with the lowest ISO possible, and typically that's around 400 (a bit lower in the snow, maybe). I'm also just heading into summer-it sounds like you're heading into winter. The days are getting much longer already. The shots I took yesterday are the ones in the yard where it wasn't raining (spring), and the camera was around ISO 400, f/5-5.6, 1/500s.
I would love to learn how to pan better as well, but I think that might be a separate technique to master-and a much harder one to do well.
I mostly get her running in circles-and they spiral in towards me, so I have to 'push' her out and get her moving faster in order to keep her moving without hitting the camera (which is another danger...lol). So the attempt at right angles is there, just not being hit very well. She moves fast enough to make me dizzy just keeping an eye on her. Which is part of the reason I think it'd be so cool to freeze that moment
As others have noted, it looks more like missed focus or too-small DOF.
I think I'd start out looking at the DOF for each shot. Check the EXIF information for each photo for focal length and aperture, and focus distance information. Plug that into the DOF calculator
Online Depth of Field Calculator and see if you are getting at least 3 feet DOF to get the whole dog in focus.
I'd also restrict how many AF points your camera can choose from (menu settings). Unless you are fully aware of how the camera decides which of many AF points to focus at, you'll find that too often it chooses the wrong one...usually whatever is closest.
And, I'd also think about setting the metering to center-weighted. I've found it usually gives the best results when in aperture- or shutter-priority modes.
Interesting calculator. Using my camera series (t5i), at 20m, approx f=100mm, and 5.6 which was set by the camera (since I was in shutter priority) I should have had 2.59 feet in focus-which is less than 3, but should still be okay. It WOULD explain why it's harder to get her in focus, though, of course my '20 feet' calculation is a guesstimate. She's not a very big dog, either. Right now the camera is set to center, single point focus (using back button) - not weighted, as its only a single point (of 9..., which the camera provides). So I don't think number of focal points gets much lower than that

I will definitely do some more accurate measuring in the yard though, and see how close I am on the guess of 20 feet. I switched to shutter priority (and 'overexpose' by 5 stops) to simplify the math I had to do for a bit because I was getting frustrating, but I could switch back to full manual....
Also, I only have the one speedlight. I know I haven't been using it very effectively outdoors, but I'm not sure how to get it closer to her without her knocking it over sprinting by. Suggestions? Indoors I have found it helps, since I can just bounce off the walls easily while she bounces off the walls.