Earlier quoted context omitted.
I'd ideally prefer to pick one that isn't used in angular things. Because non-English, non-Greek glyphs are somewhat underused for this sort of thing, and because of visual similarity to pi, I'd suggest the hebrew Het or Russian л. However, I really have no problem with continuing to use the multi-glyph symbol 2pi.
Why a multi-glyph symbol 2π when a single-glyph symbol 2π would be better. By creating a new symbol by joining the bottom-right of the 2 to the topleft of the π, we can make a new one-glyph symbol, perhaps put it next to € in Unicode. And instead of saying two words "Two Pi", we could say it as one word "Twopi", with stress on the first syllable, much like the word "teenager" used to be spoken and written as two word…
Do you also favor the almighty interrobang‽