I loved your ideas about the game. Here's my spin. Have a small kitchen scale with a doll/ puppet resembling Zacchaeus, and sack of pennies.
Put the the doll and the sack of pennies in the scale. Ask the students questions, each time they answer the questions correctly they take set amuont of pennies out of the Zach's sack. The object would be to get Zach up the tree by giving money away. The game is over when the weigh hits zero.
Also you could play this with a balancing scale and put the doll/puppet on one side and add pennies to the other side as the students answer questions correctly.