I think box to box is what's needed. I'm not sold on Frenkie being an offensive weapon. His best skills are in deeper areas for me, and his offensive runs need to be not as often. So, I'd pair him with a player like Wijnaldum, who does the legwork on both ends and has the superior ability in attack. And replace Busi with Frenkie.
The advantage of getting someone like Wijnaldum is that you get a player who can play 2-3 positions equally well. He can play in the double pivot, in a 3, he can even play as a 10 in the Pedri and Messi positions. You can even use him wide in a 4-2-3-1 probably and would do a decent job. The only question mark is how much "legs" does he have left after several seasons with one of the most intense and demanding managers around.
Also, really quality DMs are harder to find than quality box to box players. I don't see a DM on the market that would be good enough for Barca.
I think that'd limit Frenkie. He's not that good defensively. And for him to be a static DM will be hard since Frenkie thrives on moving all over the pitch. We've seen players like Busquets, Casemiro and Fabinho in successful midfield 3's work the best when they are limited and let the others handle the offense.
Frenkie shouldn't be the most offensive nor the most defensive player in a midfield 3, but rather inbetween. And Pedri clearly grabs the offensive role.
Gini would be a great signing for free. Not sure he'd work that well with Frenkie and Pedri though, at least not in the toughest of games.