the bigger and wider the ditches the longer they will last. use a
backhoe, hand digging will take forever.

you might put some perrforated schedule 40 encased in sock to minimize
mud clogging in the bottom of each ditch then use much bigger rocks for
ditch area then cover with smaller gravel.

if you put in a bunch of such ditches their filling with silt wouldnt
be so bad.

top one fills, then next one down the hill etc.

if you dont mindd overkill and a bit of added expense run multiple
perforated pipes in each ditch.

if you do a reallly great job this might last forever

run the excess water far enough away from the driveway it doesnt cause
other grief