First of all thanks for taking the time and clear things up.

In version 1.2.0 you can hold your button pressed during the grace period to ensure you're first on the next plot. We're thinking of changing this in future versions so you must press your button after the marker has moved to award fast players with itchy trigger fingers.
But don't forget when someone got a plot and the marker moves to the next one. AFAIK in the original game you could hold your fire to claim the next plot while the marker still was on the plot the other player got. So if you're changing the behaviour there maybe you need to make a difference between taken and not taken plots.
As suggested in some discussions it's possible to wait for commands from all players and advance the game more synchronously. You can make all players see the exact same scenario. It can be done in many different ways and I've read some colorful suggestions in the forum.
The drawbacks of such network models are the same though. The game can halt for all players and wait for more commands, the game can slow down, and there can be a delay between pressing a button and something happening on screen.
We think that most players would find it frustrating to press a button and not immediately move on screen. The price you pay for complete fairness is probably not worth it. So instead we've chosen to add some grace time to certain events, trying to make the game fair enough to users on slow connections.
Well, why not make it optional: Each player can decide if his movements should be client side predicted or should always reflect his "real" position on the server (and make the first one the default state). So players can decide by themselves if they put accuracy above "frustration".