Hi Jonathan, first of all, at the bottom of the well you need to have more than just a few inches of rock; remember that this well essentially must handle all the rainfall coming down within the open square footage at ground level.
If your basement has a sump pump, you will likely have drain tile running around the ouside of the basement wall right on top of the footing (meaning the drain tile is basically right at floor level of the basement).
In the center of the egress well, near the wall, dig a 6 to 8" hole with a sharpshooter or hand post hole auger down to reach the gravel/sand fill around the drain tile & fill the hole with rock. You can also put in a sleeve of large PVC pipe, then filled with rock, to help ensure the rock doesn't silt in over time. If you do this, cut the pipe level with the soil line in the well & then add your surface rock back on top. (You dont need to cut into the drain tile, just be sure your vertical drain connects with the gravel fill around the tile.) This will allow heavy rainfall (or accidents like this) to go directly to the drain tile & sump, not to the window.
As to the washout from above, you'll need to do some harder packing of the soil backfill around your extended well & ensure strong drainage away from the area until the soil has become good and tight & covered in vegetation. If this won't work for you, you'll need to excavate around the outside upper few feet &put in a plastic or rubber sheeting to prevent the infiltration/washout problem.
A good tamping of the surrounding soil & better grade should solve your problem, but again, if getting more slope is impractical, you may have to do some further digging. Good luck