I think your fighting it...I would go with it. Dig down, long(longer the better), as wide as needed & sloping at least 1/4" a foot, line it with heavy plastic in a "V" shape. Put a 6" plastic pipe(w/holes in it) in the bottom of the "V" and cover it all with gravel. Cover the gravel with a membrane to keep out the dirt/silt. That "V" trench should gather the water and deliver it in quanity at the end where you put a tank.
If the water is flowing down from the sides into the trench use plastic, if it is bubbling ^up use a membrane on bottom and top instead of plastic.
It sounds like you have most of the trench dug, plastic is cheap, so the only real cost is gravel and labor. You have more of a "seep" than a spring so I think steering it is a better way than digging for a single source that may not exist.....jmho
