not sure about clover in shade
i know imperials no-plow does well in shade and is easy to set up, just kill the existing grass roots and spread seed before a rain
you may be able to kill the trees by tapping them with a big drill and pouring round-up or stump kill in the holes
tree would did but still be standing open up the canopy for ya
drill the holes at a 45 degree angle a foot above the base of the tree, wider the tree the more holes, fill holes with your type of tree/grass root kill in the concentrated form and it should work
i plan on using this technique this year around my plots
or if you don't want to kill the trees you could just prune them with a chain saw