Monalisa

Might as well wait 1st you might receive a 2nd copy of someone in between that time.

Fionn was created to be rare prism fodder. I hear he can become a useful farmer in the distant future when his strengthening quest come in, but hardly necessary with chibi santa and karna blowing away your foes. Of course I'm a bit jaded because Fionn spooked me TWICE while trying for summer tama-chan, so I was rather gleeful to turn him into the key for Mona Lisa.

I'm in the same boat as you with my Fionn (NP2 however) about to be burned. I'm gonna wait it out until I collected those 5k mana prisms.

With the current setup I'd go for Fionn because regarding collection purposes you'll lose burning any one of them. Fionn is simply the worst out of the three, especially since you already have two farming Lancers. It's true what you say regarding Carmilla, but she is at least decent on her own.

Beowulf has one of the strongest NPs in the game. I believe he can still be useful for 1-turn boss fights.

Personally, I wouldn't dream of burning my only copy of a servant, even one I didn't use. There are events where a specific servant has a bonus, whether that is for currency drops and/or extra damage. I can't say if any of the ones you mention have such an event though.