I'm looking for an image format, unpopular as it may be, that has good quality and also good compression. After I'm done post-processing my RAWs I want to export them in a way that's shareable and practical, trying to save as much space as possible. PNG seems too heavy and JPG is quite lossy.
It depends on what you mean by "shareable" and "practical". Are you sending your images to the web, a printer, or just your own storage solution? The only practical format for the web is JPEG. If you are sending to a printer you can probably chose between TIFF, JPEG, and PSD. If you are just storing it yourself, you could use PSD, PNG, TIFF, JPEG, DNG, or your native RAW format.
Practically speaking, JPEG is great quality and sharable so there is not a real need for anything beyond that at this time. See my previous post on JPEG 2000.