OK, I have completed my tests. No Sigma 70-300 in the mix : minimum focus distance is too high, so cannot be compared with the other lenses. This remains true even in "macro" mode.
Here are the shots with the D-FA 28-105mm, both without and with TC, at 28mm and 105mm. Everything at f8 and ISO 400 .
K-1 II with D-FA 28-105, with and without Tamron 1.4x pz-AF teleconverter - Album on Imgur
Here are the shots with the Sigma 18-300mm, both without and with TC, at 18mm, 80mm, 135mm (reported in EXIF at 143), 200mm and 300mm. Everything at f8 and ISO 400 again.
The shots without TC are in crop mode, shots with TC are in FF mode.
K-1 II with Sigma 18-300, with and without Tamron 1.4x pz-AF teleconverter - Album on Imgur
You can see the full resolution for these shots by clicking on each image and right-clicking "view image".
I was shooting in live view, and focusing again for each change of lens, TC and focal length.
I ran into issues with AF with the TC at higher focal length.
For the D-FA 28-105mm, at 105mm with TC, CDAF did not work. I was able to use PDAF (switching out of liveview) to acquire focus. And then got proper focus peaking on the LCD.
For the Sigma 18-300mm, with the TC, at 200mm and 300mm, neither CDAF nor PDAF worked. I had to use manual focus. Again, I got focus peaking confirmation on the LCD screen.
So, the use of the TC definitely has a big detrimental effect on AF with both lenses - more so at longer focal lengths.
However, what I found with the IQ surprised me. I haven't spent too much time pixel-peeping yet, but so far I'm not seeing sharpness degradation from having the TC vs no TC. There is however major vignetting with the TC and the Sigma 18-300, but not with TC and D FA 28-105.
And the combination of the Sigma 18-300 and the TC in FF mode is giving excellent IQ, IMO, better than I could have expected. And certainly much better resolution than in APS-C mode without the TC.
While reviewing the shots, I became aware that there appears to be a single cat hair resting on top of 3 piano strings, very close to the center of the frame. Even after I reviewed the shots, I went back to the piano and could not locate that hair. I counted the strings in the image to see which ones it was resting on. Still couldn't see it. Finally, I took a flashlight to it, and was able to see it. It really is that small. But if you know where to look, it can be seen in almost every shot I took, even the wide angle shots.
Here is a 1:1 crop of what I'm talking about from the D-FA 28-105mm at 105mm (no TC) :
And here is a 1:1 crop of the Sigma 18-300 + TC in FF mode at 300mm :
---------- Post added 07-05-18 at 08:48 PM ----------
BTW, just looked at 4:1 and 8:1 of the 18-300 . That hair can't be seen in the 18mm shot on APS-C. But can be (very faintly) seen on the FF shot at 18mm + TC. Clearly the Sigma 18-300 lens is able to resolve more detail than the K-1 II's crop mode (about 16MP).
For reference, those piano strings are upper middle, and should be between 0.85 and 1mm according to what I read . And the cat hair looks much thinner than the string, perhaps 1/15 of that. That would put the hair thickness at between 56 and 66 microns. I may be off by a factor of 2 or 3 in either direction, but probably not more. This correlates well with what google tells me about cat hair thickness. Hard to fault the optics for picking up something this small, that I can't see with my own eyes with 20/20 vision.