Personally, I think this last one you did is quite good. It looks pretty realistic and I do not get a "beady" impression at all.
I made a few minor changes to see if I could reduce the beadiness. (But I'm not sure that I can draw eyes as well as you did here.)
I blurred the hard edges of the pupils, the edges of the upper and lower eyelids, and the base of the lower lashes.
I used a Curves adjustment to add some shadow that would be cast by the upper lids onto the eyeball.
I sharpened the iris (but not the pupil). Sharpening the iris is probably just a matter of personal taste. To me, it makes the eyes a little more alive, but I still quite like your version.
Another option for more realism is that your drawing may be too perfect. Perhaps some small veins or slight redness in the eyes. Or maybe some pores, blemishes and wrinkles in the skin. Try for a few imperfections.
Looks better than mine but fact is, nothing of those "corrections" you applied can not be done. The eyes are sold separately, there is nothing other than the actual eyeball (iris, sclera) that you can change
I went back to your original post (seems like forever, but it was only nine days ago) and you mention that this is part of some kind of game. I don't understand the game or what quality of realism in the eyes is required, but I still think that the eyes you have here are very good. Can you simply declare victory?