I have used a Hand Press a great deal. Probably more than Lee ever intended it to be. It has worked well. I use it all the time to size and de-prime brass prior to washing. It works fine for handgun and 223 or 7.62x39. I have sized 308 and 6.5C but that can be an elbow killer.
Flex has never been an issue in my use. Screw the die in so there's maybe ¼" gap between the press tab and the little tab on the handle. This should set you up about right to take the flex out of the press and get good contact between the bottom of the die and top of the shell holder when sizing.
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