I had a similar thread topic started a couple months back.
https://www.pentaxforums.com/forums/general-technical-troubleshooting/225673-...ml#post2395418
although the topic was a little more esoteric, the advice/thoughts exchanged by some of the more advanced long lens shooters here are applicable.
I even talk about my "burst" methodology, where I shoot in groups of 3-4 pics to offset handheld movement.
as mentioned by many, the keeper rate is not high, but I did manage to get a couple good images at 1/100 sec using a 300mm and 2x converter. I had more success at around 1/320 sec, but it's a balancing act between ISO and shutter speed
on top of your own technique, here's another thread I started regarding the false focus of long tele lenses:
https://www.pentaxforums.com/forums/general-technical-troubleshooting/229489-...acy-issue.html
so even having good technique is no guarantee your subject matter will be in focus (after relooking at your second photo this may be very applicable - i.e. the camera liked the grass in front and the grainy wood better than the bird)
for what its worth, I here's how I shoot:
TAv mode around f5.6 and 1/250 or higher shutter speed. I also have my ISO limited to 1250 because noise still freaks me out. When I handhold, I place my left hand on my right shoulder and brace the front of the lens across my extended elbow/upper arm. I shoot center point only, AF-S in 3 or 4 shot bursts and refocus via half shutter press after each burst. I ALWAYS use the lens hood to help fight flare.
after a week in Yellowstone and some positive results, I think I'm on the right track, it's just a matter of more practice to get higher keeper rates.