I've been giving out poker chips to players (as suggested by someone else on this board), one per meter of movement and different colors for actions. If the character is taking an action other than move, the player can still 'spend' movement chits, one chit per meter of movement. This reflects their ability to walk while doing other things.
If the character is taking a "Move" action, each chit can be 2-3 meters.
At some point I need to reconcile this against the rules' 5x maximum sprinting speed, but so far, this is working for us. Characters have enough movement to shift around the board if needed, there is a mechanism to move quickly, and the balance is working.
What I see players have their characters do is run (using a move action) to get near the action, then close more carefully the last few meters. It comes across as pretty realistic for most situations. If they want to run and engage all at once, they do a Charge action.