Just wondering if anyone has had any experience with building decks made up solely of the one faction (and neutrals)?

Not of making, but of playing against. You'll typically find yourself struggling to play around a weakness of some kind (no good EtR ICE, poor economy, poor Icebreakers for a certain ICE type) as the factions are designed to have inherent weaknesses that the influence system then compensates for.

My guess is Jinteki and HB would be best for soloing when it comes to the corporations.

For the runners i don't know, i'd say Criminals because they are my fave factions and have some real good cards, but i wouldn't be surprised if somebody told me one of the other two was better.