You want a granite type rock, not a limestone type one. Although most rocks shouldn't crumble that quick. You want some wetland plants. Not only will they survive, but they will soak up some of the water. Good shrubs are redtwig dogwood or grey dogwood, buttonbush, fothergilla, clethera. Good perrenials are yellow and blueflag iris, joepye weed (kinda hard to find but cool looking) ironweed, (ditto), swamp milkweed (ditto, smells heavanly), lobelia, forget me not, astilbe (if you have shade) sensitive and maidenhair fern, cardinal flower (again, hard to find) and monarda/bergamot. There are lots of other kids of plants, including things like swamp sunflowers, etc., but you may have to seek out a native plant nursery to find them.

I've done a lot of landscaping over the years.
The wetter a place is, the more I contour it and give it a slope. Your area looks pretty flat.
Control of water is paramount to a successful garden. Instead of just raised beds, you may need a raised path, a mulch filled ditch, and then raise beds. That's the type of contour I have in mind. You may have to go under the sidewalk and out to get rid of excess water, continuing the contour theme.
Are your downspouts contributing to the problem?
Mike

Hello?