The whole Bava Sali thing seems to have puttered out of steam. Still there are unique and special people within that tradition.  I was very impressed with one grandson of Bava Sali, Shimon Buso. But there might be others.The  daughter of Bava Sali, Mrs Buso married  fellow by the name David Buso and that is where the name come from. I am not much into the dynasty thing but in this case it looks valid to me.  My impression is it is worth the time and effort to get a blessing from Shimon Buso. [He is in Jerusalem on Shabat and Netivot during the week.]

The main thing I saw in the whole Bava Sali family was what you could call straight Torah. No "tikunim" or kabalistic stuff.
There are descendants of Reb Yaakov Abuchatzaira also around whom are certainly worthwhile to visit.

Besides that it is entirely possible the Bava Sali thing is still around. I was in Netivot for about  a year and went to Rav Montag's yeshiva for about an hour in the morning and an hour in the evening and it occurs to me today that that was a time that God granted to me a great deal of סייעתא דשמיא help from Heaven concerning the book on Bava Metzia. That is from pages 104 until page 112.

You have to do your own work to find out where the descendants of Bava Sali and Yaakov Abuchatzeira are because I do not know except for Shimon Buso.