Signet of Might vs LIS
The intended LIS mechanic is that you land as many hits against the shield as possible in a short time to make it burst. My guess is that in order to count the hits the shield has to block them (effectively counting the blocks). If the LIS was invulnerable he probably wouldn’t block anything, but state that he’s invulnerable. In this case it wouldn’t be possible to count the hits.
The best way to use Signet of Might against the Legendary Imbued Shaman imo is by activating it followed quickly by an immobilize skill so it cannot go anywhere while your party knocks its shields off (if your party is good at quickly burning the shield, an immobilize might not even be necessary and can be replaced with something better for dps). Signet of Might has a few other decent applications in fractals like interrupting Subject 6 when it goes into shield form in the middle of a burn. Signet of might really doesn’t seem to be about doing more damage during fights in fractals, but instead adding an extra element of control on tough enemies which requires good timing and proper skill usage.