I used to own a 61 SG Les Paul.A great guitar, but the main reason I sold it was its one demensionality. A great rock/blues guitar. But no decent clean tones.
Later on I made the same mistake with an SG style set neck Carvin. Great guitar, but kind of one dimensional.Not as gritty pu's as the Gibson, but still kind of the same. A great hot, overdiven humbucker tone, and thats about it.
At least a les paul will clean up for a nice warm, clean, and smooth jazz tone, or a least the last Epi LP Custom I owned would. Never could get that out of the SG LP or the Carvin. But the pus on the epi LP had less output, not nearly as hot as the 61SG LP or the Carvin.
Not trying to talk you out of it, just an observation. If you also own a longer scale Fender style guitar w/single coils, then your set with just about all your bases covered.
As for the Faded Special vs other Epi or Gibson options, I can't really help you there. I'd suggest just go play em and decide.