Sorry DK for not getting back to you sooner.
Your plan your the grade 9' feet out is good, the further the better if you cannot get it totally graded away. Your lucky that your front yard slopes away so well it gives you an easy place to send water.
If you grade 1/4 in 1' then the weed fabric will be fine, it's obviously not going to stop water but your grade will push the water away from the home.
The rock or mulch or whatever your using for a garden cover can go straight over the weed fabric, you could still plant some small plants or shrubs in this area, that too would help with any extra water.
As for the "flatness' of the grade, the easiest way by hand in challenging soil is to get it as close to graded with your hand tools, shovels etc... then get some nice top soil and rake it over the area to smooth out the grade, then lay your sod. If your not laying sod on any of this area then just hand grade to 1/4" in 1' doesn't have to be pretty then cover with your ground cover material.
No matter how you put it though, this is pure "grunt" work by hand.
Bottom line is.....as long as the base ground slope is away from the house, it doesn't matter how deep your mulch or river rock is, it could be 3' deep against the house and 6" deep 4' out, (the depths are for explanation only.....
) the water will drop through the rock to the ground and then be sent away from the house and on it's merry way to the street.