Another press you ought to consider is the Forster Bonanza Co-ax press. More winning match loads are put together on this press now than any other. It doesn't have a turret. Instead it uses thick die adjustment rings that slide in and out sideways. You change dies for each loading operation, but because they slide straight in and out, you don't lose time turning threads in and out or re-checking the die adjustment. The change is almost as quick as spinning a turret one position. You still wind up performing each operation on all cases as a batch rather than loading progressively, but most people loading for accuracy don't mind the extra time since they are inspecting each round at each stage anyway. The press has a universal sliding V-jaw shell holder, so you don’t need separate shell holders. I load .223 and .308 in it changing nothing but the dies. The press comes with oversize jaws for 45-70 and other extra-wide chamberings.
Not many things cause measurable accuracy changes by themselves, but the seating die is one that can. I use the Redding Competition Seater Die exclusively now. Every general purpose seating die I've used will allow bullets up to 0.008" or more of runout at the neck, including the standard Redding seater dies. The Redding Competition Seater Die has never allowed more than 0.002" of measurable runout in any round I’ve loaded with one, and that was in military brass that was 0.002" thicker on one side of the neck than on the other. Out of my Browning A-bolt, this translated into taking 1.25" groups down to 0.75" at 100 yards.