They can handle the quick ones just as easily if we don't have a passing game. Just kick them a couple of times early and slow them down, like what Watford just did to Mane. He can expect a lot more of that treatment this season. He is a tough guy for his size, but he'll have to learn to pick his battles.
Pelle is not the reason the backs are lumping the ball forward. It's that there's no link between the midfielders and the forwards. When you play with Long, Pelle, Rodriguez and then two rather defensively-oriented midfielders the space between the lines is too big.
Only Mane is really capable of receiving the ball deep and then dribbling with it. But even then he is much better at using his pace and trickery to drive directly at people hoping to cause chaos as opposed to orchestrating an attack. Which is not really a criticism of Mane, just saying his best role is probably to play off a striker. If you give him the ball at midfield he'll just outrun all of our other attackers and then have no one to pass to.
I don't think either Davis or JWP are currently good enough to be that attacking midfield link, at least not if they're the only true midfielder in an attacking role. If we don't bring in a winger, I think we have to look at using Tadic more.
I get that Tadic slowed down a lot as the season went on, but I also think our Route 1 style of play and general ineffectiveness coincided with him not playing and us using forwards or speed merchant types like Elia. Earlier in the season, Tadic and Bertrand and Tadic and Pelle were both good partnerships, and when you have that, then you can make pretty triangle shapes and have all those angles to work off etc.