For a well-rounded workout and build, you actually want to adjust your grip on a regular basis when doing pull ups. IOW: do close, neutral, and wide as well as palms toward you in the neutral position. You don't have to do these all at one workout if you don't want to, you can switch it up.
And to clarify on the "building muscle, losing flexibility" front. This is not a forgone conclusion (see Tom Platz for reference). If you don't stretch, you lose flexibilty (unless you are just naturally flexible, but that doesn't sound like its your problem). Remember to stretch when not injured, and get creative. Your bicept is meant to rotate your hand, so do stuff like put your arms out in front of you and slowly rotate your hands around (good beginning stretch after overworking your biceps). Good luck to you.