after importing animation to unity, with only bones, the default avatar pose is quite different from with a skinned mesh attached, resulting different quality when retargeting animations. you can see the comparison in the picture, the only difference is the attached mesh, all other attributes are the same. is Unity doing something differently in these two situations?
I understand the bind pose is factored into importing the character somehow. That being said, I ran into a similar issue with a skeleton with a mesh on it. For some reason some of the animations came in with weird rotations on the joints that were appearing in the animations themselves despite them being exported with proper alignment. When you import and configure the rig you can go into the Rig–>Configure and manually correct the rotations and the animations will correct.
Hope that helps.
Also, I noticed you have a 3rd bone in your spine. I too have that in one of my models. I think it may be giving me problems during animations where precise alignment of the hands is imperative. Do you notice that unity is not responding well to the extra bone? I have mine included in the avatar mask to be calculated, but it seems to still be causing problems. Not sure. I suppose the only way to find out would be to recreate all of my animations with just 3 bones in the spine… which would suck.