2 years ago I also bought a set of large and small Dillon tubes for my LNL. It came with extra plastic pieces for both ends. After looking at them a bit, I modified the Hornady tubes by by driving out the plastic ends and slipping on the Dillon's pickup ends. Looking at them now, I would just nock off the clear plastic (or blue) drop end of the Dillon's and drill a through hole directly into the tube for the clip. This way it will self center automatically.
As I was typing this, I decided to try out the above mod. Getting the drop end off the Dillon tube proved challenging, I finally "warmed" it with a plumbers torch and it came right off, destroyed of course. A hair dryer wasn't hot enough but a heat gun probably is, but I don't have one. I'm sure there is a better method. I drilled a 5/64 hole about .150 from the end. The hole in the Hornady tube is roughly 3/32 but it was missing from my index. No matter, the 5/64 works fine. I filled the small primer tube with 100 federal sp's. Once pushed out of the tip, there is room for about 3 or 4 more primers. Then I filled it with 100 rifle primers. Less left over room but it took the whole box. Oh yeah, no more wiggling on the LNL.
<edit>Another thought. It would be a whole lot easier to slip a short piece of vinyl tubing (a bushing) over the Dillon drop end for centering. I don't have any vinyl tubing handy but next time I go to lowes or home depot I'll check it out.</edit>