Change your monthly backup to the 1st Friday of each month.
Weekly backups can occur on 2nd, 3rd, 4th, & last friday of each month.
'Should you have three media sets?' A general answer would be 'yes' for a GFS rotation. Keep in mind, rotation sets are really for defining how long you want to perserve the data. So ideally your Monthly backup media set has a very long overwrite protection period (months or years), your weekly media set OPP would be less (Weeks or months) and your daily set would be even less (days or weeks).
However, in your initial post you indicated you have 20 tapes, and you change tapes everyday. On average there are 20 weekdays in a month, so every month you would rotate through your entire set of tapes. -I'm not sure a GFS rotation is required for something like that.
However, if you changed tapes at the beginning of the week for the incremental jobs, and left that tape in all week, then changed it Friday for the weekly/monthly job, you would use only ~ 8 tapes a month, and that would give you more retention, and more justification for a GFS rotation.