I know this is an old thread, but just in case you're still curious...
The only SLS-free toothpaste that I have come across that is also ADA-approved is Sensodyne Fresh Impact. Sensodyne also has the ProNamel line of products that don't contain SLS, but their other toothpastes do. I have sensitive teeth as well, so Fresh Impact works great for me.
Here's the toothpaste on the ADA site (Fresh Impact does NOT have SLS, but ~~Fresh Mint does)~~: https://www.ada.org/en/science-research/ada-seal-of-acceptance/ada-seal-products/product-category/product-report?productid=5243&company=GlaxoSmithKline+Consumer+Healthcare&category=
ADA acceptance may not be that important, but I figured I'd note it just in case. Whichever SLS-free toothpaste you choose, make sure fluoride is in it.