This old rumor rears it's head every so often on these forums.
Carp, your problem is the problem with all Dillon presses. The press is made to load a bunch of shells and when used for just 1 the floating die design shows its ugly head. There is a kit made, not by Dillon, to fix the die head in the press and keep it from wandering around side to side and up and down. Basically threaded inserts are put into the die holder and bolts are run down through the keeper pin holes through the die holder fixing it in place. It would add anohter 45 seconds to a die change over. Was thinking of getting one of the kits myself. An ad for the kit was in either Shotgun News or American Rifleman all the way to the back this past month.
Yes the tool head can move up and down a tiny amount in it's slot. The point has always been, it's movement is always consistent. Side to side? come on now that's really stretching it! Proof in these pics;
Reading before the press ram is raised,IE in neutral/zero
Reading is .013, in case you can't read it. My point is it is .013
every time!
This was while loading 45 acp with 200 RFN lead boolits. Lee carbide dies, no lube used, factory crimp die in last station. The die in front of the dial indicator is the powder check die base.
That kit is a solution to a non-existent problem.
Another point; You will be drilling, tapping parts that cannot be returned to original, except buying a whole new press frame. Think long and hard about this, "so called problem"!
Added to that, if this is done by someone with a hand hole shooter,(drill motor), I'd bet those holes will
not be in perfect alignment. Short of setting the bare press up in a milling vise, indicating everything level and square, you will not have those modifications straight.