| Matthew Vertz |
After having just played a 4th level investigator (admittedly this was hastily constructed so I may have missed some key decisions/mechanics) my biggest qualm is the reliability of study. I like the notion of some sort of success even in failure if it has to be a roll. I think of starfinder's envoy and how many of their abilities work in some fashion even in failure.
If it has to be a successful roll with no wiggle room for failure, I'd prefer to have to make the study roll just once for the initial effect, and then have an action that refreshes the effect each round for next attack so long as I don't change the target of the study. This would meet in the middle on the rolling aspect while still forcing me to participate in the action economy every round to maintain it. It would also alleviate the frequency piece of the originating ability. I could spend all three actions trying to initiate my Study if that's what it takes. Since this option would make the study reliably maintained, the rate at which the investigator gains studied strike dice would likely have to be slowed down.
From there the ability would give me a minor boost to my damage output per the studied strike, but more importantly would be used as a corner stone to provide my party with several advantages as I shared my deductions and predictions based on what class feats I've taken and how I choose to employ the action economy, similarly to the OP's suggestions.
