Learn English – “at the time” and “at that time” usage and differences

I suspect that there are several word-plays going on here. In American myth and folklore, the full moon of each month is given a name, such as Wolf Moon, Storm Moon, Harvest Moon, Hunter's Moon, etc. A blue moon is a rare occurrence that happens about once every 2-3 years when a single season (three months) experiences four full moons; the third full moon in a season with four full moons is called the Blue Moon. There is no full moon specifically called the Killing Moon.

An Old Testament poem tells us that there is a time for everything under the sun; a time to give, a time to take, a time to heal, and a time to kill, etc. Calling something a killing time or killing moon would mean that somebody's or something's death is imminent and unavoidable.

I suspect the author in that sentence hesitated between often and most of the time: he wanted to indicate that it was helpful very, very often; but he didn't want to go so far as to say that it was helpful more than 50 % of the time, and so he chose a somewhat cowardly expression in between. I think he would have been better off choosing either often or most of the time, or perhaps very often, though I don't think the added intensity of very is really necessary.

Most of the time is an expression indicating that something happens more often than not, usually much more often.

Much of the time I would normally only use where you could not substitute often, a simpler word, which is the case especially when it is about a large chunk or chunks of a period, not merely a frequent number of times.

They arrived early at the aeroport. They had wanted to spend their final hours in romantic embrace, but they were busy looking for the right papers and documents much of the time.

This means that a large part of this time was spent looking for papers, but "large" could be anything from 1 % to 99 %; if I used most of the time, it would mean that more than half of the time was spent on it.