With some further googling and hunting around on SO, I have put together a solution.
ggmap(map, extent = "normal", maprange=FALSE) %+% W + aes(x = lon, y = lat) +
geom_density2d() +
stat_density2d(aes(fill = ..level.., alpha = ..level..),
size = 0.01, bins = 16, geom = 'polygon') +
scale_fill_gradient(low = "green", high = "red") +
scale_alpha(range = c(.00, .25), guide = FALSE) +
coord_map(projection="mercator",
xlim=c(attr(map, "bb")$ll.lon, attr(map, "bb")$ur.lon),
ylim=c(attr(map, "bb")$ll.lat, attr(map, "bb")$ur.lat)) +
theme(legend.position = "none", axis.title = element_blank())