I feel like this should be an easy thing, but every time I slap an overlay down - a sign, road, poster, whatever - it's blown up and ugly. How do I ensure that it stays in the correct proportions as I scale it down to a size I need?
Positive. You can resize overlays using the handlebars, but the proportions get messed up if you do and often they don't start out in the correct proportions.
You can open the VTF to find out exactly what proportions the overlay is, but most tend to fit nicely in a square.
Are you moving the individual vertices using the overlay tool, or resizing it with the selection tool? You should be doing the latter (with texture lock turned on) for resizing signs and stuff you don't want distorted like signs. In general any of the wall decoration sort of stuff should scaled down to either 50% or 25% of the default placement size. Should be obvious which one looks right once you do it.