Ran some quick numbers for a post on reddit, wanted to add them here in case anyone is interested.
Also i am unsure why you mentioned a 2 slot requirement for offhand voltaic + mjolnir. I only use one slot for elemental. Unless you meant both an active and a passive slot, but in regards to blood main ive never can it so i could not give a solid answer.
Fun with fuzzy math:
To throw some numbers into the equation my power attacks hit for about 7k and crit for about 17k. My basic attack hits for about 3.5k Effectively every power attack i do has double the damage of a basic attack, in my gear, currently.
Now lets look at a 20 second rotation with a 1s GCD. Full salvo is going to use 2.5 seconds (effectively 3). 1 of these global cooldowns will be shell salvage. and so far 2 will be reloads. This leaves us with 15 seconds to make attacks. 3 of these attacks will be offhand 5 energy power attacks to maintain energy neutrality (10 energy regen on offhand every 20s. 5 energy from Shell salvage). This puts us at effective 12 global cooldowns for use with shotgun attacks.
Regular shotgun would be 6 Power attacks. 5 basic attacks. 1 reload, and leave us with one shell. Using my numbers that would be 42k in Power attack damage 15.5k in basic attacks. Assume 0 crits for simplicty. This puts us at 57.5k
Double barrel shotgun will be 9 power attacks and end the rotation already reloaded at 6 shells ready to start over. 63k.
Worth noting double barrel gives me currently an extra 584 damage on each power attack which is added into the weapon damage, is not a separate hit, and is therefore buffs crits even higher. Pulling this out of the regular shotgun means it is actually at 54.5k and any other proc needs to add 8.5k damage over 20 seconds to break even. A plasma forged shotgun adds a baseline 6k in total across 3 hits. Assuming 25% chance to proc You are going to get a baseline of 2 procs from your shotgun rotation, and likely 3, possibly 4 during your full salvo. Average this across three rotations and the extra damage is about 8k total, still short of the double barrel math if not by much. (25 dps)
A spes gives a 20% chance for an extra 2k damage. Assuming You spend 6 shells on shell salvage, 6 shells on opening shot/full salvo. and 11 shells on attacks per the rotation you are going to get about 4.2 procs. best case scenario not counting any kind of stacking. Or about 8k total damage.
Shotguns in this game are very close, but assuming no crits double barrel will eek out a small win. At the high end currently my Raging shot crits for about 17,000. My basic attacks would crit for 8400. Every power attack for me is worth the damage of two basics. By doing nothing but power attacks my damage will always exceed a build alternating powers and regulars by the value of a at least a single power attack every 20s, or about 175-420 DPS. The power/basic rotation will also not reset until 22s once it has used the 6th basic, and reloaded.
TLDR: Double barrels will give slightly better results, rising as gear improves, in exchange for a more interactive rotation and the numbers will be higher but within spitting distance of the current meta BIS.
Other factors such as more usages of Depleted uranium shells, less over-capping on dragons breath, and more usages of the shotgun belt all serve to skew the numbers further into double barrels favor.