I have a lot of issues with the OPs shooting conditions,
As many have said, with stationary birds on a feeder, and a tripod, why is the OP shooting at 1/1250 and wide open. It makes absolutely no sense.
He should be shooting at less than 1/400 and stop down a stop or two.
It is also unclear whether he has SR on or off, and on a tripod using SR can make things worse,
In fact, with lens combo he is using, he should hand hold the shots. For stationary birds, you can go down to perhaps 1/200 hand held reliably providing you have proper technique. If you are really good, you can get about a 50% keeper rate at less than 1/100.
If the OP wants to see the limit of SR, look at the link below
Pentax K 300mm f/4 samples - PentaxForums.com
The first two shots, are shot with the K7 at 1/40th. I was free standing, no post or other support to lean on, and simply kept my arms tight to the body one hand at the extreme end of the lens, and the other on the grip so I could hit the release. The camera was tight against my face, and I took several slow breaths before the shot, tripping the shutter while exhaling slowly. The first shot is the full frame, the second is a 100%crop with no image resizing it is a JPEG right out of the camera with no sharpening or processing. It was done this way to be able to upload on the site at the time without getting resized upon upload,
My approach these days is as many others have posted, is to use Tav mode and let the ISO go where it needs to, my two current shooting bodies are a K5 and a K1 MKII and the iso limit is set to 6400. I shoot with some better lenses these days than the K300 and 1.7x AF adaptor, but for me, I prefer a sharp image with some grain over a bad image due to wrong settings. I also shoot spot focus, unless doing BIF where I use on the K1 the center 9 focus cluster.
I think here the OP just didn’t have things set correctly