A few years ago I was having a problem with my reloading some 7x57 brass and some 30-06. Very similar to what your having happen. My press had been set up for 25 years on the same heavy bench. Turns out that after 25 years there was a very small bit of flexing in the bench even through the bolts were still tight. I got a piece of 1/4 inch steel plate and set up my press on it and bolted all to the bench and the problem disappeared.