The water has to go somewhere, so no matter what you put in the hole, it’s going to come back out. Can you take a photo from further back so the whole area is visible? Are the larger rocks small enough to move to work on the area? How big is it? Without seeing it, I’m wondering if you can make a “stream bed” with large, medium and small sized rocks to minimize erosion and dig a dry well at the bottom to take the resulting water. Or a drain to divert it elsewhere. Otherwise, I’d consult a professional who can see the site in person for advice.

You should try filling the holes with 3/4" gravel, this will hold together but will have enough air gaps between the rocks to allow water to pass through. Pea gravel usually just washes away with storm water.

You can funnel a little paver base into the holes. It firms up and holds well—but it’s ugly so you want to follow with a little sand perhaps (allows drainage and fills gaps) and then nicer pea gravel, sometimes labeled as smaller river pebbles, depending on the overall coloring and texture.

I’ve practiced xeriscaping for the past 12 years and have an impressive 50’x150’ rock garden feature/path and hydrangea garden in my front yard (in Chicagoland) so I’ve dealt with freezing, raining, drought—you name it.

Hi Bob, Pea gravel is so lightweight that it's really easy for minimal flowing water to pick it up and carry it downhill. You are on the right track when you started talking about larger (heavier) rock. It will stay in place a lot better. Lastly, if you choose this option, choose a type of rock that is triangular in shape and not round. Triangular rock locks itself into place and stays put much better than round rocks that have big void spaces and are susceptible to rolling out of place.

Maybe one should incorporate asmall waterfall feature in the drainage area? It sounds like it wants to be one.