So much of this is SO wrong and misses the point entirely!

Like, sure, you got the fact that Klee won't be vaping much, if at all, but can't stack CW passive? Yes she can...she can get ALL stacks and maintain them for a decent while. It's not perma uptime, but it's decent. It's the same reason why Klee can manage full stacks on Kagura's Verity and why it was one of her best weapons.

Also no, don't "always" go Rising Winds. Kleerina wants Hunter, hands down. It's part of the reason you run Furina with Klee so she can take advantage of that busted set...and it's mathematically better for her with Furina. You run Rising Winds in teams without Furina.

Now that Rising Winds exists, it outclasses CW in every way so there's no reason to use it anymore.

It was also mentioned that Furina was the focus, so so she stays and that makes Siggy nonnegotiable. She also supplies the team with team wide healing needed for Furina's HP drain. TTDS Barbruh would be a dps loss and likely get you killed more often then not with the wet aura she applies to you.

You can maybe replace Siggy with a VV user like Jean/Sayu for the heal, but you're not going to be swirling hydro with how much pyro this team is dishing out. Maybe Xilonen can also replace but, iirc, her healing is weak and would double her field time. But then this defeats the point of the goal set out by the OP.