Regarding the asteroid scenario. It seems to me that if you have a formal mathematical model of the laser and the asteroid then you can build a safe math oracle to solve the problem while if you want the AI to figure out physics by itself then "correct x coordinate" can be dangerous by exploiting an unintended mechanism of influence on the world.
It seems like the purpose of the asteroid scenario is not to come up with ways of deflecting an asteroid, but as an example system in which two uncoordinated AIs (pardon the pun) can minimize impact in an interesting way.
A write up of the various ideas we've had around reduced impact AIs:
https://www.dropbox.com/s/cjt5t6ny5gwpcd8/Low_impact_S%2BB.pdf?raw=1