I tweaked it a bit and came up with this, which does what I want it to do. It was the conditional not for bp_is_my_profile() I was missing, for future readers.
I know this is an old post but I searched and searched for a solution to this and finally found one today, so will repost here for others. The solution does require installing Gravity Forms, and then you also need to install the GF User Registration Add-On (check the Add-On item in your Forms dashboard menu). Create a registration form with Gravity Forms, then add a User registration feed, and not only can you opt for automatic password generation but you can also map fields to Buddypress 🙂