Muddy alley between houses - Advice Needed

Have you tried a creeping groundcover that will grow in pretty deep shade? Something like pachysandra will likely grow in this space. You might even try planting a whole bunch of mint; it is very shade & moisture tolerant and spreads like wildfire.

Do you need to be able to walk down the alley regularly, or is it more of a dead space?

65x6 is probably $2k for concrete and form place finish. Split dat. Be done.

Had this issue at a previous house. Installed a drain which ran I ran to the front yard, then filled in the area with pea gravel, and put some 1x1 paving stones for a walkway. Mine was only about 30x5 area. Looked good enough and worked well while only costing a few hundred dollars and an afternoon of work for my dad and I.

Depending on which rock you choose, you could diy in the range of $300-$400. 4 yards of rock and some landscape fabric and 1 length of metal edging. You could also drop a flagstone path if it’s an area you need to traffic. A much cheaper option, and I’ve done it for the exact problem you discuss, is to substitute pine straw for the rock. It’s actually decorative and you could do that area for under $50 and it’s very easy.