I suffer from SD and used to have the permanent layer of dead skin like you describe. I couldn't see it when it was dry, but as soon as it got wet, it was very white and had an almost sticky texture (meant I couldn;t go swimming due to the embarrasment).
I scraped it off with my nail and whilst my skin went very very red immediately afterwards, it did calm down to leave smooth skin, with no dead cells.
I probably shouldn't have done this, but I was desperate.
Since then, I've been washing twice a day with Garnier Deep Pore wash and the dead cells haven't reformed and the problem has gone away. My skin is very dry and flaky after washing, but if I don't apply moisturiser afterwards, the natural oils eventually (after a couple of hours) seem to do the job of a moisturiser and the flaking dry skin goes away...until the next time I wash.
Hope this helps???