We know that Taim's cronies got promoted and were taught things the regular Asha'man were not but I don't know if they were automatically the most powerful. They were the most ambitious, probably evil but one had to want to join Taim to get an invite and it seems from what little we have seen of the Black Tower that there are quite a few dedicated who do not like the way Taim does business and they chose to side with Logain instead. Quite a few of these were strong enough to shield and bond the Aes Sedai strike group without too much difficulty.