I also gave them a choice of a different assessment, which was an argumentative essay about a US Supreme Court case- only 3 out of 105 students opted for this. Most of my feedback through out the unit had to do with similar cases and writing arguments, so I assumed(again) many students would choose this option.
I have proven one thing in these few years; my students are not very driven to cheat. I guess I should be worried if everyone scored 100%.
Standards based grading would improve student self direction and motivation.
Go play around with Jumprope (on line standards based grading program) and see if it will work for me.