Stefan, inside that 4-way there is a tiny ledge near the bottom just above the side case cutout, and sometimes it makes a case hang or even fall crooked. If you drop a 1/2" thinwall inside Lee's tube supplying that smaller sized opening you prevent cases from even feeling that ledge.
Weight may help, but I doubt it, but even so Lee's thing with feeding the last four primers and the last four cases is annoying. There's not a lot of weight available with the last four....primers or cases. As 9mmepiphany said, drop everything as vertical as possible, and if it starts falling forward, backward, or sideways, you WILL have problems. On the bottom of my 4-way (pre 3D-printer days) I raised my 4-way to account for clear shaped tubing forced in from the bottom, to direct the columns down, and prevented opening too soon, allowing sideways deflection, and big trouble. What the vids I just posted showed is what minimum dia. downtube with ONLY forward cutouts could do......but before I 3D printed parts I used the clear tubes with shaped side openings as the picture below shows....
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They may be ugly, but they worked because cases could not fall sideways, being "kept" by cutouts that were forward of the side diameter lines....
the later 3-D printed versions more clearly show this....picture below.....(left cutout too far back to the Diameter line and did NOT work, the right one is cut as far forward as possible and it did work with a full heavy stack or the last case in the stack...no matter.)
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Below a 357 pistol version cut forward that works every time. (Which I also use just as successfully on the 6000.
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Below: Close-up of the cutout....notice the case is "kept" sideways and not allowed to go any way but forward......and about that.....forward pushing of the slider has to be from the bottom or very close to it or it can fall forward......I know from experience....and it's why I'm spending the time to help you NOT experience it.
Mostly it is the next case in line that causes the problems, if it's not "kept" long enough.
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You don't have to have a printer....but you do need thin-wall clear tubing in various diameters. Someday Lee is going to see the light and make them perform this well out of the box.