OH, not slow!
Yes, that's the right sandwich, I believe. Alicia I'm sure would have some fantastic advice here. It does cut into (but not through) the crease pad.
As far as the crease pad being too short, I honestly don't have an answer. I have used my Baskets and Blooms die probably 100 times, and I've never had it cut on the creases! I just use my plates, not the crease pad.
Are you cutting cardstock or DSP? One thickness? Usually my score lines turn into score "cuts" when I try to cut too many thicknesses.