Don't water the moss. The worms will either go deeper if possible or move to wetter spots.

thanks-- currently the ground is wet due to rain, so there's not much I can do about that. And of course, it's the rain that is also encouraging the moss to spread, which I desperately need-- after 2 plus years, the yard still looks like a dirt lot in most areas.

Sounds like you need to work up a profile on your yard.
That is using graph paper plot out the yard with inclusion of overhanging trees (large circles), shrubs (smaller circles), presence of rocks, ornaments, walks, driveways, paths, and whatever is present. See link below.
You need to determine the general type of soil you may have, which I am wildly guessing is probably either a red or a gray clay soil base ????? Check this link >
Soil types maps

Part of the problem for noninvasion by mosses into the bare areas may be due to a combination of the type of moss species present, the amount of exposure to the sun or lack thereof, the nature of the soil.
There is one methodoly that may be of use to you. I am surprised that Moss Acres did not mention it. Using a grow felt system. Check out this link > New Moss Gardening

This method might even keep the worms from messing things up as you are growing the mosses on top of a mat that sits on top of a plastic sheet. Check the site and ask Rick questions if it interests you. I grow my many mosses in containers and experimented with Rick's method. Here is a page on that experiment.
{{gwi:600425}}
Also since you are in NC you may want to contact Mossing Annie! Here is Annie Martin's link > Mountain Moss

Perhaps the above info will help you achieve your goal of a green yard!
Here is one of my mini-"yards"
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Here is a link that might be useful: Draw your landscape plan

Thank you for this detailed response! I'll be following up on your creative suggestions.