Thanks for trying 
As mentioned, I’ve experimented with various methods and some of them have almost made the cut, but haven’t found one I’m perfectly happy with just yet. It is a problem that I always keep at the back of my mind, so one day I’ll crack it
There are a couple of ways I think you could go at this. The first would be to implement a turn-in-place animation before the unit moves along the spline. This would be a general UE4 thing so you should be able to search for how to do this. However, for ATBTT you would want to make sure you do it as part of the move action (or queue it as a separate action before movement). In any case, make sure it is appropriately queued so that it animates at the appropriate time. Check out my videos on the action system if you have not done so already.
Another method that might potentially be both simpler and better, but which I would have to test out, would be to change the movement spline in BP_Unit. When the spline path is generated, normally the first spline segment would be angled in the direction of the displayed spline meshes. However, you should be able to angle the first spline tangent in the direction that the unit is facing. I believe this should let the unit begin movement in the direction it is facing and smoothly turn into its spline path. There might be some unforseen jankyness at certain path angles and lengths, but that would have to be tested. I might test it myself one of these days when I have the time.