My theory is that grass will out-compete moss IF it has enough sun, AND the soil has enough organic matter AND is at all well-drained.
Do you have a free source of organic material for compost or mulching? If the whole lawn and all beds need compost, make-your-own would be much cheaper than buy trucks-full.
Maybe just sheet-compost leaves on top of your raised beds for now. That would smother weeds AND feed the soil.
I hope you love living in this area! I enjoy seeing all the fields and nurseries from the road when I drive to Snohomish (the town) to get to Steubers. I think it is something like "Seattle Hill Road" that has a great view of the valley.
We almost bought a house there, up on the hill, but it was old and broken down AND too expensive for us.
