I don't really know Solomonoff induction or MWI on a formal level
You know more about it than most of the people talking of it: you know you don't know it. They don't. That is the chief difference. (I also don't know it all that well, but at least I can look at the argument that it favours something, and see if it favours the iterator over all possible worlds even more)
If I know that the universe seems to obey rule X everywhere, and I know what my local environment is like and how applying rule X to that local environment would affect it, isn't that enough?
Formally, there's no distinction between rules you know and the environment. You are to construct shortest self containing piece of code that will be predicting the experiment. You will have to include any local environment data as well.
If you follow this approach to the logical end, you get Copenhagen Interpretation, shut up and calculate form: you don't need to predict all the outcomes that you'll never see. So you are on the right track.
it doesn't take any extra code to predict all the outcomes that you'll never see. Just extra space/time. But those are not the minimized quantity. In fact, predicting all the outcomes that you'll never see is exactly the sort of wasteful space/time usage that programmers engage in when they want to minimize code length - it's hard to write code telling your processor to abandon certain threads of computation when they are no longer relevant.
Series: How to Purchase AI Risk Reduction
Another method for purchasing AI risk reduction is to raise the safety-consciousness of researchers doing work related to AGI.
The Singularity Institute is conducting a study of scientists who decided to either (1) stop researching some topic after realizing it might be dangerous, or who (2) forked their career into advocacy, activism, ethics, etc. because they became concerned about the potential negative consequences of their work. From this historical inquiry we hope to learn some things about what causes scientists to become so concerned about the consequences of their work that they take action. Some of the examples we've found so far: Michael Michaud (resigned from SETI in part due to worries about the safety of trying to contact ET), Joseph Rotblat (resigned from the Manhattan Project before the end of the war due to concerns about the destructive impact of nuclear weapons), and Paul Berg (became part of a self-imposed moratorium on recombinant DNA back when it was still unknown how dangerous this new technology could be).
What else can be done?
Naturally, these efforts should be directed toward researchers who are both highly competent and whose work is very relevant to development toward AGI: researchers like Josh Tenenbaum, Shane Legg, and Henry Markram.