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Makes no odds: if it's for sale elsewhere, it can't be advertised here.
Having a fixed price sale here and an auction elsewhere, the chances of someone getting fucked are considerable.
No doubt you'll take the highest price, which means that whoever buys it, could have legitimately bought it cheaper and possibly leave another gazumped and disappointed buyer.
So that's two people fucked-over for the price of one.
Decide what you want to do: an auction or a fixed price sale. No auctions on LFGSS, so it'll have to be eBay if that's your choice.
Either way, LFGSS ads should be exclusive: if it's advertised for sale on here, then it can't be advertised elsewhere and vice versa.
FWIW it is a nice bike, but you'll (almost always) take a kicking selling a complete bike: split it to get more of your money back.
Actually it is against the rules of this forum to sell a bike here if it is being sold anywhere else.