Recently got a 4K TV and obviously the 480 can't do much at that res, but are there any tweaks that will enable me to enhance its 1080P output for a 4K screen?
Use the GPU scaling setting in Radeon Control Panel to upscale the output to 4K rather than rely on the TV to do it. GPU hardware upscaling is almost always preferable to letting your TV do it as it generally produces a better image and does not introduce input lag.