How much movement between the driveshaft and transmission is acceptable?

I have been tracking down some vibration or harshness, most evident on acceleration at low speeds, but cropping up at other times as well. The u-joints all seem tight and smooth, the center support bearing has no slop besides what the cushion allows. I bought the parts to replace these, but they do not appear to need it yet.

When I grab the driveshaft at the transmission and shake up and down, it has some slight slop, felt as a barely perceptible clunk. I would assume that any movement there is bad and calls for replacement, yes?

Also, when I rotate the driveshaft with the transmission in neutral, there is some freeplay before I can feel the drag of the transmission. That is, I can spin the driveshaft back and forth a degree or so before the splines contact. Is that normal?

Have I found the source of my rumbling?

Thanks,
Sean