The first paragraph consists of a very long and confusing sentence which at least seems to deal with the timeless decision procedure.

The timeless decision procedure evaluates expected utility conditional upon the output of an abstract decision computation - the very same computation that is currently executing as a timeless decision procedure - and returns that output such that the universe will possess maximum expected utility, conditional upon the abstract computation returning that output.

I think this needs rewriting so it doesn't sound so circular - and only mentions the word "conditional" once.

It seems to me that we can just say that it maximises utility - while maintaining an awareness that there may be other agents running its decision algorithm out there, in addition to all the other things it knows.

I think the stuff about "conditional upon the abstract computation returning that output" is pretty-much implied by the notion of utility maximisation.