Hi, Ryan. 3-8-12 overwrite periods are correct. If you keep all your backups in one location there is an easy way to achieve your goal. Set gfs schedule to overlap yearly, quarterly and monthly dates (and overwrite periods 3-8-12). If a date overlaps, the backup will be placed to the higher media set. Schedule for example: first sunday of the year for yearly, first sunday of first month of each quarter for quarterly and first sunday of each month for monthly. As a result you will have 1 yearly backup for year 3, 3 quarterly + 1 yearly (which makes 4 total) backups for year 2, 8 monthly + 4 quarterly backups (12 total) for year 1.
If you move different media sets to different locations then you need to make a schedule without overlapping (first sunday Y, second sunday Q, third sunday M for example). And actually I don't understand how is it possible not to keep 'newer' counterparts. Only if you keep your 3-year-old-full-backups on hard drive and place them on tape after 3 years.