Just to make sure we have the main goal in mind here, I've interpreted "bypass[ing] the electronic AWD feature" as meaning you're looking to bypass whatever software-driven traction system you've got (ABS, VDC, TCS, ABLS, etc.) on the truck with a mechanical LSD. If so, my quick response would be that if you can find a suitable LSD, bypassing any system wouldn't be necessary: the system would just be supplemental to the device's functions. That is, the system would only kick in after it determined that a LSD (if it existed) was allowing enough slip to satisfy detection logic via sensors.
Otherwise, if you do mean to bypass AWD, you may need to expand on what function you're referring to. The All-Mode system on the truck already has the means to bypass the mode simply by turning the dial to 2WD, but that option seems out of context to the questions.
Either way, I'd just focus on the LSD part for now, if that's what you're really after.
Admittedly, I don't know much about R51, but I can infer enough just from FSM data (https://www.nicoclub.com/nissan-service-manuals) and part numbers. Follow along...
The 2005 FSM indicates you've got an R200 rear final drive.
A parts cross-reference indicates that the side gears in your differential (38423-0C000 -> 38423-0C00A) are also used in 2003-2008 350Z cars and 2005-2010 Frontiers, Xterras, and Pathfinders. That means the splining between those vehicles are the same.
The differential carrier (38421-0C000) for those trucks were all the same, and since the Frontier and Xterra have C200 rear axles, and yours has an R200 rear, it means those differentials are the same. (R200/C200 compatibility was also true on pre-MY05 trucks/SUVs/cars, but MY05+ R200/C200 are different from pre-MY05 versions.)
From prior research just the other week, I can also confirm that the C200 open carrier from a 2.5L D40 Frontier is the same as a 350Z, and they too shared the same side gear.
All the above vehicles use the same carrier bearings. I presume more parts to be identical.
The end result is that, in theory, all the differentials from 2003-2008 350Z and 2005-2010 Frontiers, Xterras, and Pathfinders with R200 rear diffs (G35, R51) or C200 rear diffs (D40, N40) are all interchangeable.
If that's true, a Quaife QDF13L LSD for 2003-08 350Z/G35 with VLSD should work in the truck. My full technical assessment is available here: https://www.clubfrontier.org/threads/rear-axel-swap.368234/post-3903321, but the abstract that's relevant here is:
If you decide to read into that post further, please enjoy my bashing of some idiot. There's also some technical "talk" about what Nissan calls a system versus what said-idiot calls a device, just to clear up the differences in traction systems and devices.