I think what you describe is normal -- but then, I've never had "normal" vision. It could also be your prescription . . .
A story that might help. . . For a long time, when I went to the eye doctor & they had me read a chart, I worked hard at it. I didn't relax & read what I could, I tried hard to read as far down as I could. Apparently my glasses prescription reflected this. When the doc got in some new technology that somehow gave them a different way to evaluate eyes, the device showed a different prescription was needed. But, they always use both "the machine" and the patient's response, so they gave me coaching on how to read the chart -- basically, just relax & don't tense up the eye muscles. Now my prescription is optimized for not straining instead of straining.
None of this will let you focus for a long time. Shots are best taken, as you say, after 5- 10 seconds of aiming. This works well, though. If you are shooting fast & holding off, you'll take them that fast. If you are waiting for a particular condition, you don't have to constantly re-aim, just aim once & watch the flag -- you don't have to strain to watch the flag . . .