Next time out put your boat in gear and let out all the line with nothing tied to the end (just a raw end). Once all of the line is out, drag it for a minute, then reel it all back in. This will allow the line to relax all the twists out, then it will lay correctly on the spool as you reel it back in. The tension will also insure the line is spooled tight and even.
I have tried all the tricks in the book while spooling spinning reels, and the one foolproof way to get rid of line twists is to use the method I describe above. Braid will not act as bad with line twisting, but I still do this just so I know it's laying on the spool as best it can. I'll also do this a couple of times between respooling too.
If you're not living on the edge, you're taking up too much space!