I like the way you are thinking through this so as to only have to do it once 
It's quite possible that just a 'shallow' ~6" trench just filled with gravel (or series of trenches joined together to 1 or 2 drainpoints on the big slope) would suffice to keep the water out of your pool area. I do however, think that some sort of pipe or drain in the gravel would facilitate the flow and allow for better drainage. I also think that wrapping the weed block fabric around even just a gravel bed is a good idea - it'll stop all but the finest sediment from clogging the path you set up and is essential if you use some type of drain (and the fine sediment will be washed out when you've got a good flow going through it).
What you may want to consider is a main trunk line (with the 3" side holed drain pipe) leading down to the big slope and a couple auxiliary, shallower, trenches feeding into it. Remember that water takes the easiest route (path of least resistance) and also seeks the lowest place it can get to (hence the need to have the downward pitch on the trenches/ pipes) - keeping these 2 things in mind will prevent puddling in your yard/ pool area. Using the weed block fabric will keep the trenches/ pipes free of dirt and roots which could congest them.
Unless your neighbor Noah is collecting 2 of each animal and buying Home Depot, Lowes, etc. out of lumber, you should be able to handle normal spring snow melt off and spring and summer downpours
As always, keep running your plans/ ideas by us :-D
Oh yeah... when you get down to doing the project, could I ask you to please keep track of expenses, time it takes and some pics (I know you're good with the camera and know how to post the pics ) - it might be a real help to others here who have or may encounter the same problem. Thanks!
It's quite possible that just a 'shallow' ~6" trench just filled with gravel (or series of trenches joined together to 1 or 2 drainpoints on the big slope) would suffice to keep the water out of your pool area. I do however, think that some sort of pipe or drain in the gravel would facilitate the flow and allow for better drainage. I also think that wrapping the weed block fabric around even just a gravel bed is a good idea - it'll stop all but the finest sediment from clogging the path you set up and is essential if you use some type of drain (and the fine sediment will be washed out when you've got a good flow going through it). What you may want to consider is a main trunk line (with the 3" side holed drain pipe) leading down to the big slope and a couple auxiliary, shallower, trenches feeding into it. Remember that water takes the easiest route (path of least resistance) and also seeks the lowest place it can get to (hence the need to have the downward pitch on the trenches/ pipes) - keeping these 2 things in mind will prevent puddling in your yard/ pool area. Using the weed block fabric will keep the trenches/ pipes free of dirt and roots which could congest them.
Unless your neighbor Noah is collecting 2 of each animal and buying Home Depot, Lowes, etc. out of lumber, you should be able to handle normal spring snow melt off and spring and summer downpours
As always, keep running your plans/ ideas by us :-D
Oh yeah... when you get down to doing the project, could I ask you to please keep track of expenses, time it takes and some pics (I know you're good with the camera and know how to post the pics
) - it might be a real help to others here who have or may encounter the same problem. Thanks!