Excellent Idea! My Amazon Prime account makes me automatically turned off by delivery charges. $6.99 is too steep per package for me (mainly due to the low cost of the items I purchase), but I would definitely enroll in some tier type pay package. $X for Y total deliveries or $1.75X for 2Y total deliveries.
Speaking of which, does Amazon batch Amazon.com deliveries with Amazon Fresh deliveries? Might make sense if you don't mind waiting an extra day for a package to get routed through Amazon Fresh's warehouse in exchange for knowing it'll be out in front of your door in the morning.
Looks like it's $6.99 per delivery, not necessarily per package. Perhaps they can accept & store packages for a couple days, if you know you've got a string of them coming, and can wait until they're all at the luna wearhouse?
edit: clarity