*Uber thick, crest necky with fat deposits and thick throatlatch
Not conformation faults. Personal preference (and of course, a dietary issue which you can and will fix when it becomes important to you)
The thick throat latch thing is a myth that just won't seem to die. Lipizzaners are all thick throat latched and it does not affect their ability to flex at the poll. What IS important is how far apart the jowls are. They need to be a hand widths or there's not enough room for the neck to fit between them, and THEN the horse would have an issue with poll flexion.
*He's overweight and needs conditioning overall
Yes, he is, but not a conformation related.
*big body, little head
Again, not a conformation fault. And in fact, I think your image of your horse is a bit skewed here.
Fault heads would be eyes placed on the front of the head, a face excessively dished that it interferes with breathing, parrot mouth, short mouth, etc...
A 'small' head is not a fault as long as sight, hearing, ability to chew food properly, hold a bit, etc... is not affected.
*No decent withers to speak of
He's has a 'low' wither. Not a fault. As long as the wither can act as a fulcrum point, it's not faulted. A mutton wither is a conformation fault because the wither can't do its job.
We might fault him for the wither not carrying back further into the back, but that would be nitpicking.
*A bit cow-hocked in back
Nope, not seeing that at all on him. Looks fine to me.
Hard to say for sure because the angle is a bit off on that view, but that left hind may be a bit crooked on the third plane. But we'd need to see a few more pictures to confirm that.
And yes, horses ARE SUPPOSE TO TOE OUT BEHIND. It is a fault if they do not. The toe out behind should be equal to the stifle turnout angle. The reason for this is that if the stifle pointed straight ahead, when the hind leg came forward, the stifle would hit the ribcage. So the stifle points out so it can clear the ribcage. This then means for the hind leg to be straight to the stifle, that hind foot better point out at the same angle as the stifle, or the horse is crooked legged on the third plane.
*He seems to stand under himself a bit too much in front (at least in these pictures)
Yes, he does. Not a conformation fault, but a postural issue that you can fix.
This type of stance happens when one or a combination of the follow things happens:
Horse being downhill built
Horse being ridden on it's forehand
I'd like to see a new set of pictures, making sure the photographer stands directly in front, directly behind and directly center body for all the shots. I'd also like to see a top view from poll to dock.
From these pictures I'm really not seeing a lot to not like about this horse, but I suspect a couple of things and would like to verify them before commenting.