So let's say I'm confronted with this scenario, and I see $1M in the large box.

So lets get the facts:
1) There is $1M in the large box and thus (D xor E)=true
2) I know that I am an one boxing agent
3) Thus D="one boxing"
4) Thus I know D/=E since the xor is true
5) I one-box and live happily with $1,000,000

When Omega simulates me with the same scenario and without lying there is no problem.

Seems like much of the mindgames are hindered by simply precommitting to choices.

For the red-and-green just toss a coin (or whatever choice of randomness you have).