Finally getting to doing an update on this with new DA-1.4x AF AW teleconverter included alongside native and old MF 2x TC. Don't have access to Pentax A-1.4xS from @georgecape, but impression is that new DA-1.4x is very similar performance, just with all the convenience of AF.
The performance of the DA*300 with these TC versions is remarkable, and it seems to confirm my view that a good TC just magnifies lens defects. And the DA*300 doesn't have much of that. So TC IQ degradation is minimal. Obviously the IQ suffers a bit from addition issues of subject motion, atmospheric distortion and camera vibration as the magnification becomes enormous.
Then started playing with double up of 2x and 1.4x not expecting too much. Was I wrong. The IQ seems to hold up remarkably well, and the old Saitex A-2x is not too bad.
Got to say, the prospect of an 840mm f/11 lens (equivalent wide open f/4) at this IQ is attractive for some uses.
The view comparison only cropped horizontally. (ie full vertical FoV)
And then a zoom in on the angle graduation plate with each image resized so that the view is the same number of pixels in each case (600x600 from 2.8x TC as default view)
And then a real target bird who was kind enough to be sitting there for the whole show
1/500s, f/4 (f/11 eq), ISO400