Why do my pulled handles keep cracking at the attachment points?

The S cracks are almost never a scoring problem, so you can stop blaming yourself there. In my experience they come from one of two things: the ends of the handle being either wetter or drier than the wall when you join, or the joint not being compressed after you stick it on. Scoring and slipping gets things to stick, but compression is what actually welds the two surfaces togather. After you press the end on, I wiggle it slightly side to side and down against the wall, then run a finger or a wooden tool around the seam to smooth and pack it in. If you can see a raised lip of slip at the edge, compress that too or it'll crack right along the seam as it dries.

What fixed this for me was putting the pulled handles and the mugs under the same plastic together for a bit before joining. If they sit side by side wrapped up overnight they end up at pretty much the same stiffness, and my crack problem basially went away. I also stopped trying to attach when the mug was still soft like you describe, the wall was denting every time I pressed. Now I wait untill it's firm enugh that my fingerprint barely shows, and the joint holds its shape instead of smearing. The wiggle-and-pack step the poster above mentioned is key too, I do the same thing with the end of a wooden rib.

Same here on the overnight wrap trick, it made a bigger difference than anything else I tried. One thing I do on top of that is drape a little piece of damp paper towel over just the ends of the pulled handles before I close up the plastic, since the tips dry out first and that's exactly where my cracks always showed up. I also stopped attaching at soft leather hard and wait until the mug passes the squeeze test, no dent when I press a knuckle into the wall. Figured out the hard way that a soft wall just flexes instead of gripping the joint.

One thing that helped me a ton was supporting the wall from the inside with a finger while I press the end on. That way you can get a solid join without smooshing the mug, even when it's a bit softer than ideal. I also stopped trying to make the handle ends super long. Shorter contact patches are way easier to weld down properly, and mine used to crack right at the tip of the long tails every single time. Sounds dumb but it fixed it.

On the slip thickness, since that hasn't come up yet: I used to slop it on thick, and I eventually figured out that a fat layer of slip is basically its own little clay body sitting between two others, and it shrinks at its own rate and cracks along the seam. Now I score, paint on a thin wash with a cheap brush, and wipe away anything that squishes out past the edge, beacuse that excess is exactly where my old S cracks lived.

For your firmness question, I go by the fingernail test, meaning the wall takes a mark without a raised burr around it, and the mug doesn't wobble when I press near the rim.