I like the Lyman lathe type, it has a universal case holder, no collets or shell holders to deal with. I believe you can get an adapter to hook up a cordless drill to it. I have an older RCBS(well my Lyman is 30+ years old) that uses collets, the new ones require a different shell holder for different cartridge bases. I have a drill hook up for that and it is great for big batches, I run 500 223s at a time and the drill is a god send. The problem with collets is variations in the size (roundness) of the case head will vary the case length, a problem avoided by the lyman, and newer RCBS.
I think, but am not sure the zip trimmer uses some of the trimmer parts you have, but I have not had much luck with Lee over the years except their dies. My Lyman and RCBS trimmers have served me well having run tens of thousands of cases, replacing cutter heads with carbide ones when they dull.
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