Dave, hate to say it but I'm not sure you're going to fix that with a shovel and wheelbarrow.
![Smile :) :)](https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f642.png)
the pics don't show a lot though, maybe you can. Possible solution may be a crown drain ( French drain as you planned) with live pole drains on top. The crown drain is kind of a rainbow arch, it can catch groundwater across the whole area you're trying to control, avoiding your earlier issue of the spring changing exit points. The live pole drain likewise for any surface flow. Every now and then we have a spyder hoe passing by Calgary if you want to throw money at it and have it dug by machine, the spyder is amazing for where it can go and what it can climb.