Mine have the small amount of side to side movement like you describe, and always have. Its nothing to worry about.
The way I've always tightened them is to move the pushrod up and down with your figers until you can't anymore, then tighten it down a half turn past that. Your way works too, it's just that it's easier to tell if it's stopped moving up and down then it is to feel the resistance on a small cylindrical smooth object like pushrods.
Hope this helps, good luck
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NMRA O/C 9516
NA pumpgas stickshift 347 10.65@125.6, 6.73@100, 1.41 60ft
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