Calcium or Lime should help kill off the moss I would think. I'm new at this so I hope someone more experienced chimes in here for you.

Moss is a first stage plant Ma Nature grows to cover bare soil. While many people think it grows on compacted, shady, acidic soils that are too wet I have moss growing in full sun on loose sand as well as crushed dolomitic lime and on the concrete blocks that are the house foundation.
Look at your soil this moss is growing in to determine what needs to be done to make the soil good and healthy so it can grow what you want there. A good reliable soil test is a start so you know what the soils pH is and what needs to be done to correct that, if anything and dig in with these simple soil tests,
1) Structure. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. A good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2. Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.
to see what else might need be done.
Mostly where I have moss growing the soil lacks adequate levels of organic matter.

I agree with kimmsr re the soil test before liming -- I also live on the west coast, and the conventional "wisdom" here says that our soil is acidic, so all the lawn companies automatically put down lime twice a year without testing.

I had my soil tested this spring and it revealed that I have a neutral (7.0) pH, so if I had gone ahead and limed like usual, it would have made it worse. I also have lots of moss - regardless of the lack of acidity.

I've read a few articles from well-known Pacific Northwest gardeners that it is just something we need to accept here due to the moisture levels (and any shade), or at least deal with on a yearly basis.

I can't say whether feeding lawn food will help the moss grow. But apparently if you apply ferrous sulphate (or other moss killing products found in garden centres), it kills the moss which makes it much easier to rake out than when it's alive and green.