Yep. Once L has established overlap and given room and opportunity to W (as W has just become the give-way boat), then L can begin to assert her rights. Proper course applies in almost all instances following the overlap.
If I were the overtaking boat, I'd be looking for some seperation during the pass to minimize W's shadow and get clear as quick as possible. Passing close to leeward and at speed is risky - you can have rights and still get flipped on, run into, broken, etc. If I'm getting passed to leeward, especially on a reach, I'm looking to see what I'm dragging. <img src="http://www.catsailor.com/forums/images/graemlins/tongue.gif" alt="" />
ps - If it were your 'proper course' to come up during the pass, why didn't you roll them high instead? Safer.