The ShuffleIt developers are Dominion enthusiasts, and it really comes out in the design choices made for the game. Everything is geared towards people like themselves: Serious hard-core Dominion gamers who strive to decimate their opponents in every confrontation.
The problem is... you have completely FORGOTTEN about the most important group in your would-be customer base: casual gamers
Everything about the structure of this system favors tournament-style play where winning and losing matter, a lot. There's no consideration given to times when folks just want to log in, play 3 hands in 20 to 25 minutes, and then walk away.
Solution: Make "unrated" games played as Speed Dominion (similar to Speed Chess).
Speed Dominion would be exactly like regular Dominion, except that any time it is "your turn" a timer will be rolling on-screen, displaying the number of seconds which you have been in control of the board and other players are simply staring at the screen waiting for you to take action. Every 100 or 120 seconds, that counter resets to 0... and you gain a Curse card.
Alternately, you could just measure the Player A time and Player B time. Once one player has accumulated 2x the amount of play time as the other, the games ends and the player who used 1/3 of the time wins and the player who used 2/3 of the time loses. This would require a caveat that no game would ever time-out until at least 5 minutes of total play had occurred (game total, not per-player).
Just like Speed Chess is a totally different kind of game from Tournament Chess, Speed Dominion is not Dominion. Speed games should be limited to unrated games where statistics are not recorded, or a 3rd class of game should be created where only the results of Speed games are computed in the overall score. Leave the tournament play as-is.
Of course, the "serious" Dominion players on the system would just change their matching preferences to refuse Speed games. That's fine; let them have their 3-minutes-per-turn hands where they calculate all the mathematical possibilities and go through the painstaking process to draw all 35 cards of their deck into play every single hand.
That's fine, but I don't want to sit at my screen staring at someone else playing their hand for 80% of the experience.
Give us this way to avoid dealing with slow-rollers, whether they are rookies or hacksters just trying to mess with us, or 53.00+ ranked players who want to slow down and do everything PERFECTLY.
I, personally, don't want to play with either of those classes of opponent, and this is a way to make sure I don't have to.