The 270 Win has a long neck. You need to lube the inside of the case necks to get smooth resizing when pulling that neck expander through the neck. Just the nature of the beast. I use a RCBS nylon neck brush with CLP on the brush, a very light coat. I lube every other case neck. Works out fine. I've been reloading for the 270 Win. since the early 1970's. Love the cartridge. Took a lot of game with it over the past 45+ years.
If you don't want to use the neck brushes, try using a Q tip with a little case lube / oil on it. Test it out, see if it works.