You could skip the fat sills, but I'm not a fan of skipping the sills entirely. What I mean is instead using a short sill. This gives you a definite location to put your posts, and provides a good means of resisting any tendency of the posts to move out at the bottoms.
Around here many barns built around the turn of the century are timber framed, and built on a continuous, solid block or stone foundation. The fat sill is often gone on these barns, and instead the posts are tenoned into a narrow sill -about 2" to 3" high resting on the concrete blocks. It's minimal, serves no real purpose structurally as the foundation does that. It just keeps the posts up a bit and keeps them in place.
I am afraid not to use any kind of a sill, I have seen the results of that in many 100 year old barns in my area. These barns all had sills originally but at some point more recently the sills were cut out of some of them for assorted reasons. The result is in a lot of these barns that the posts have spread significantly at the base. Not a good thing to be sure.
And I am weary of anchoring posts into concrete with steel connections. That just gives me the willies. I am afraid of what that could look like 50 or 100 years down the road.
