I like your idea for the lithium grease, as well as Perry's for the silicone. I went down to the basement and got a spray can of each, and began reading. The can of lithium says a lot about using it for outdoor hinges, but I'm assuming what they mean is just the usual metal-only ones.
Have you had any concern applying it on your hinges where that little rubbery compression thing is between the hinge bolt and the spring? I do not know if lithium is ok for rubbery parts; I am NOT trying to be a smarty pants.
If you apply a certain way (e.g., with a cotton swab or something) I'd love to learn of it. I used to use silicone on my pop up camper risers, but never had to do any lubricating to the door as it never squeaked.