In my opinion it would be better to reduce outstanding shares with a huge buyback program as the first step even if it doesn't help PPS climbing at the moment but the more they buy back the better for the long time.
As a second step I would pay a cash Divi one year later to the remaining shareholders after I have finished my buyback program, that would skyrocket PPS with a much lower freefloat.
As a third step I would sell the cheap bought shares from the buyback program to institutional investers on a much higher PPS!