I've spoken to a few folks about this but there is a way, not too difficult once you get the sequence down, to solo the bridge after the lamp section (Run Forrest Run). After watching the videos and putting a good bit of time into trial and error I was able to get the loot for both my Titan and Hunter. Only got shards on one toon but the other picked up the Raid Gauntlets. This method is using the cannon launch off of Lamp 2. If interested, let me know and we'll figure out a way to view my run or I can point you to the videos so you can use it.