Vigilants of Stendarr are the lowest ranking members of the Order. The whole thing would be very Templar-ish - the armour the knights wear would look like Crusader-era Templar armour, minus the crosses. Their little temple would be expanded into a large fortress, for example, and Vigilants are actually only the bottom tier of the hierarchy. What I envision is to turn the Vigilants of Stendarr you see walking around into a joinable faction, the Order of the Vigilant Knights of Stendarr.
Even the Companions are tainted by the whole Werewolf thing, and plus despite their 'honor' thing they are still mercenaries. Other than the College of Winterhold, none of the factions in Skyrim are really 'good guys'. However I think it's a good idea nonetheless. Now, what I'm about to describe would be incredibly complex and large, and I have not the patience to figure out how to make this an actual mod.