Hello, I researched previous "Ask Extension" questions on this topic as well as other Oregon State University information.  If you live on the west side of the state, you have more rain, and you will have moss!  I live over on the east side and moss/slugs just not an issue for us, ha ha.  Here is some info for you:

Ask Extension previous questions/answers:

Removing moss from Brass Buttons (Leptinella squalida) groundcover #446521

Asked April 06, 2018, 1:32 PM EDT

I have replaced the lawn in my yard with Brass Buttons groundcover. Unfortunately, weather conditions last winter has left if overrun with moss. In a small area I can dig out the moss with a fork, but this year there is far too much for that approach. One can find many brands of lawn chemicals with moss remover. Would these be safe for use with the groundcover? If so, how bad are they from an environmental standpoint?

Multnomah County Oregon

Expert Response

Moss competes well with many plants in our environment including turf or low groundcovers, as you are discovering. I am currently allowing the moss to take over groundcovers in the shady, damper parts of my landscape. It looks great in my opinion.
To encourage the other plants to dominate, give them enough sunlight, and summer watering. Sometimes soil ph needs to be adjusted, or fertilizers used, much the same as recommended for turf. See the details in this article from Oregon State University's Gardening Tips. "If you mind moss, get on board with preventative measures": http://extension.oregonstate.edu/gardening/2017/04/if-you-mind-moss-get-board-preventative-measures
Read any lawn treatment product labels carefully, and don't use one that mixes purposes. Check a spot to see how your groundcover responds. Anything with "weed killer" is likely to kill your non-grass groundcover plants.
Again, see the article. Killing the moss you have won't truly fix your problem because it will just return. Work on discouraging it, or living with it.
A slightly different angle to deal with moss is to grow taller plants that will cover or shade it out. Heathers, ferns, and Arctostaphylos uva-ursi are possibilities height-wise. You'd have to choose plants also based on light conditions, soil type/drainage and personal preference.
Jacki D., Master Gardener Diagnostician Volunteer (Washington, Multnomah and Clackamas Counties) Oregon State University Extension Service Volunteer Metro Master Gardeners (http://metromastergardeners.org/) Replied April 10, 2018, 12:07 AM EDT

When is the best time of year to apply moss killer? - Douglas County

A: If you want to kill moss on your roof, wait until we have a forecast for no more than a 1/2 inch of rain late in the rainy season so you don't wash the product out into the street and into the river. I usually apply sometime in May. Products for houses can be either zinc or ammoniated salts of fatty acids.

If you are putting moss killer on the lawn, wait until there is a forecast for light rain. After the rain stops, go out and apply the material on the damp moss. Make sure there will be a couple of dry days after the application. Lawn products should contain iron as their active ingredient. -- Steve Renquist, OSU Extension horticulturist

"If you mind moss" article:

https://extension.oregonstate.edu/news/if-you-mind-moss-get-board-preventative-measures

Methods of moss control:

https://bryophytes.science.oregonstate.edu/page18.htm

Moss in lawns:  

https://solvepestproblems.oregonstate.edu/lawn-problems/moss

https://extension.oregonstate.edu/video/managing-moss-lawns

And here is a chemical approach that is mentioned in OSU agricultural sciences website:

chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://agsci.oregonstate.edu/sites/agscid7/files/ag-ed-sci/bierma_moss_melt.pdf

Cindy Brown, OSU Sherman County Extension, Moro OR