What if Glorfindel joined the fellowship to Lothlorien?

[Tuor in Gondolin]

Interesting point by Boromir about Elladan and Elrohir being chosen by Elrond.
I had always assumed one of them would have been Glorfindel (and Tauriel? )
--- ducks bricks---

But assume you're an Elrond advisor and he's unsure. Who would you pick.
What about another dwarf and a junior Rivendell elf so both northern elf
polities are representative. Dwarfs would be useful if some of the company tried
to get through to Mordor (and I believe Aragorn was going to include Gimli
in the core company to get to Mount Doom.