Using the RCBS Rock Chucker press. I think I know what you mean about gaming over and no, I don't think mine does, I think it's set up so that the stroke bottoms out just before the linkage starts to go backwards.
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... <Much solid advice in this thread, and as many different ways of doing the precision loading proceedure as there are individuals doing it.

To reply to OP, this is the way it works for me.
I don't shoot BR, my ammo standards are 1.5 thou. TIR or less, and 1/2 MOA from my 6.5x55 or .308 precision rifles. Shot from bipod/bag, in the field.
The reason cam-over works better than just trying for consistent handle pressure, is because cam-over does not vary ... the press is the same every time.
Far as I know, the Rock Chucker does cam over. Have a close look at the ram, with no die in the press, see if it reverses direction very slightly at the end of the handle stroke.
Collet's are
Very Touchy to set up(ask fellow member Gootch, who's Rock Chucker once sent a Lee Collet aluminum top cap, clean through a ceiling tile!

)
If it's the die's adjustment that is preventing cam-over, you need to back it off till it will, then make(very)fine adjustments by feel to find the sweet spot for sizing. Too much, and vertical ridges/impressions show on the neck. Too little, and neck thickness variations also vary the tension on the seated bullets. Some will be loose.
They aren't all perfect out of the box, dissassemble and look for burr's between the four fine slits in the collet piece, also rough surfaces on the two angled parts that force the collet closed. Also, some have fat center stems, that won't size enough. "Tuning" may be required.
I cycle mine through the die twice, with a 1/4 turn of the case between strokes. > ...
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I as for the case lube, I don't use a ridiculous amount but I will lube the case on a pad before running them through the press.
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... <I don't use any lube when loading with collet's.> ...
The issue with seating the brass is most notable with new brass but I have seen it with fireformed brass. Anything from the collet not closing the neck enough to it feeling quite tight. I'm wondering if I should set up the collet for so I can put more force on the case.