Instead of using the team bar to split ties why not use the value of the last card played? With higher movement cards splitting ties over lower ones. This would give some degree of control over the outcome and add a risk/reward element to card play. I tend to find players are more accepting of bad luck when it is due to their own action rather than a raw card flip.
- edit for clarity
Please feel free to implement this in your games as a house rule. If it goes well come back and provide some information for us on how it works.