What would happen if in all tasks where the out come is never immediate, the GM does not let the players see the roll? If this takes away the fun of rolling their own dice, let the Players roll it, keep it in a cup or container and conceal it until after the result would be apparent. Only the GM would be allowed to see it. The GM will then describe the result. Bring a lot of dice if you plan to do this. In such rolls, the GM must be able to describe the task as easy, challenging, difficult or hard, or very had or nigh impossible.
Characters with the same appropriate skill in a given task may be allowed to have their own opinion in the course of action. They also get their own roll and it will also be hidden from them. They will not know if they are wrong or right, and it is purely up to the PCs personality to act on this information.
Predictably, players will err on the credibility of the lead character, based on that character's level of skill. this is not meant to confuse the players, its supposed to give them insight into their own judgments and the probability of them being wrong or right.
Note: This system is appropriate only if the GM has a already streamlined resolution process.
Courtier Edits. I realized I was a bit too vague with some suggestions: specifically, how a PC's strategy skill affects the Players execution. I tightened the bolts a bit, anyway these are all in constant flux and are subject to revisions as I plug the holes of these ideas.