Looks to me like you might be better off installing french drains at strategic points, like where the biggest ditch is.

Do you mean (in the last photo) to the right of the line of boulders? I'm not sure how that would work.

You'd need to study the pattern of waterflow during the next downpour. Water will find the tiniest of dips really quickly. You'd put a perforated pipe under the gravel at the lowest point, have the open end of the pipe exit in your woods.

A problem with the perforated pipe suggestion is that the gravel is mixed with very fine powdered rock (of the same type) which would probably fill up the holes in the pipe, and the water in the downpour might simply wash the gravel right over the top of the pipes.

Or, perhaps, fill the gaps between the larger boulders with concrete and imbed the existing gravel pieces in it. What do you think?

I was thinking about using some of these:

https://www.supplyhouse.com/NDS-864GMTL-5-Pro-Series-Channel-Drain-Kit-with-Galvanized-Steel-Grate?srsltid=AfmBOoraYRs6njUajdqYy8Ti4nyEvoHdegYkgXZQI4ZPcBciVVOD83N1KGs

but I would need a lot (100 ft = 30 lengths = about $2200).