It is a little more complicated if you keep the idea of two rolls. Consider the idea of one roll resolution. You roll 3d6 to take an action and do not roll separately for effort.
If you are rolling d4, then you take the lowest of the 3 dice.
If you are rolling d6, then take the middle number of the 3 dice.
If you are rolling d8, then take the highest of the 3 dice.
If you are rolling d12, then take the top 2 of the 3 dice.
You then apply your effort modifier to which ever dice you pick. This means a high attempt roll is more likely to result in a high effort result. Now, this does mean you can roll something like 1,6,6 on a basic effort action and it can be kind of a letdown. If you want to avoid this, you could also say every 6 gives you +1 effort. So, even if you roll 1,6,6 you still get 3.
On the upside, this system opens up a lot of dice pool manipulation mechanic. For example, stress dice similar to the most recent alien RPG. I am thinking they are extra d6 added to the roll and you take the top 3 dice to check vs the target, but perhaps you have to take the stress dice when calculating effort? Adrenaline can push a character beyond what is typical, but the results become more random the less calm they are.
On the downside, this kind of rolling has completely different probability distributions that I have not even thought about the implications. So use this at your own peril. It just strikes me that this type of rolling could help tell the story, but avoids the numberless narrative dice that I do not enjoy.