Sill plate wet in corners
Looking at your original picture, I can tell the moisture is coming in near (or at) the top of the floor joist not the bottom, because water won’t “wick” up that floor joist uniformly like it is showing. (In fact, it seems wetter along the top of joist than middle of joist.)

Therefore, I’d concentrate on the joint at the top of the 2x8 trim. 

According to your drawing, it looks like you’re relying on caulking at the top of the 2x8 to keep moisture out. That means the caulking has to be perfectly installed and well maintained. Even then you can develop problems. (Look at at knot in the first row of logs and notice that moisture can penetrate into the knot and run down behind the caulking.)

We usually use a piece of counterflashing that laps over the 2x8 about 3” and extends into the wall void about 3” with a 1” hook in the up position. (Make sure the flashing is no more than 10’ long, for expansion, and each piece laps about 6” and is sealed with mastic where it laps.)

Also, I’d install that 2x8 on peel and stick  moisture barrier and extend it under the counterflashing and over the subfloor, if possible. 

Also, we don’t like caulking at the bottom of the 2x8.  We like moisture to run out if it gets behind the 2x8 at the joints, corners, etc.