Ooh, I second Bay's suggestion for Treesje. Their unglazed, matte leathers are very soft, e.g. the current grey leather in the Marley!
Botkier also has some great lambskin bags this season, and Botkier's lambskins are usually really soft too. If you're unsure which Botkier leathers are lambskin and which are cowhide, you can check out their site, click on any style, and click on the scrolldown menu for colour options. It states the type of leather of each colour option. The Venice hobo (or maybe even the satchel) sounds like it might be right up your alley!
Linea Pelle also always has great lambskin leathers, wonderfully soft as well. They definitely have some totes this year that fit the bill (zipper closures, long strap drop for shoulder wear), particularly in the Dylan collection!