Some games have a system whereby instead of resetting the timeout every time a player makes a decision, it keeps a running clock and every time a player makes a decision, it just adds a small amount of time to the clock. So perhaps if the clock started at 5 minutes, but only added, say, 30 seconds for most decisions.
EDIT: No, even that's too much. 10 seconds? And you can't ever bank more than 5 minutes.
Hearthstone actually did this very well. You only have X time for a turn. If you run out, you will only have 10-15 seconds on your next turn to make a move. Then you return to full turn time. This way if you want to slow play, you can only make the person wait so long because you will eventually run out of time anyway.
Hearthstone's system works okay for Hearthstone (though it's not perfect, since it allows too much time for early turns), but for Dominion it would be a disaster. There's way too much variance in how long turns take. Like LastFootnote proposes, some capped cumulative combination of time-per-turn and time-per-action is probably the right way to go for Dominion.