Those peristaltic pumps are usually pretty strong. I know that the Neptune DOS is rated for up to 24 feet of lift. I would not go with any smaller diameter tube though. I don’t think it will make a difference in terms of the pump’s ability to push water up and it will probably be easier to clog. My water mixing and storage station is in my garage and I have a DOS pump that pushes water up into my attic, across the attic floor, then down through the wall into my living room tank. About once a year my 1/4 inch NSW line seems to get clogged with calcium deposits, although I recently switched to a polyethylene tube instead of a vinyl tube and that one seems to be more clog resistant.
Oddly my OSW line has never gotten clogged and that’s an even longer run as it goes from the tank, up inside the wall into the attic, down into the garage to the DOS, then back up into the attic and over to the laundry room, then down inside the wall to the laundry drain.