As much as I dislike having to ask for help, I'm at a loss for this one.
I first added the 74HC14 and removed the current reduction circuit on the Y axis driver. This actually made it perform worse. The motor would turn, but much slower than it should have been and along with the sound of it missing the majority of its steps. I then removed the optocoupler, which provided the fix I was after; the axis moved smoothly and, as well as my short testing could show, took care of the loss of steps. I then tried replacing the 1000pF cap with a 151pF (I didn't have any 100pF caps readily available). No noticeable results over the removal of the opto, but it didn't make anything worse.
I then applied these changes to the other two axes, with the only difference being that I desoldered the transistor and capacitor that made up the current reducer circuit completely. The Z appeared to work fine, however the X would stall if it got anywhere near the speed it should have been going (90IPM), and would still audibly miss steps even at under a third of that speed. Stranger still, after further pondering and testing, I discovered that, should I attempt to move the Y and the Z at the same time, the X would try to move, too. All it would manage is a grinding noise and slight turning in whichever direction it was last moved, but it was a consistent and repeatable effect.
I've checked every connection and solder joint a dozen times by now and I'm certain I didn't screw anything up as far as that goes. The only thing I haven't tried that I think might be applicable is grounding the heatsink, but I was under the impression that that was mostly a safeguard against a cascade failure between chips...
Any help? At this rate, I'm ready to grab a couple new TA8435H chips to replace what I burnt on my first controller.
EDIT: Well, damn, looks like the problem was one of the wires sitting funny in my breadboard. Fiddling with it fixed things.
As a side note, thanks much to the OP. I'd have been very sad had I not been able to fix this thing. As it stands, this thing now goes FAR faster (up to double the original 90IPM I was getting if I use whole stepping) than it used to on the old controller. Good times.