As has been stated, there's really nothing to be gained from removing the front cover that you can't more easily determine from your RPO build codes and VIN. My thoughts back then were related to some apparent rumors/misinformation related to the front ring gear having been attached to the front carrier by GM in such a way that the entire carrier would need to be replaced to change the gearing, instead of just changing the ring and pinion gears themselves, as one would expect.
I went around to some driveline and performance shops at the time and no one had any definitive information (including supposedly knowledgeable GM industry contacts) on what, if anything, was available for the front axle in '19+ GM trucks. The rear axle (RPO codes listed further below) apparently has aftermarket gear sets available, regardless of axle manufacturer (AAM or GM). It's the front axle where all the difficulty comes into play, as I'm sure you know. I basically gave up back then and decided to wait until the pandemic's effects on industry were a little further behind us.
(As a side note, I still intend to replace the rear OEM limited-slip carrier in the rear with an Eaton TrueTrac, as there's no better time to do it than during a gear set change. I believe the TrueTrac will be more robust/reliable than the OEM solution, especially with the increased mass and leverage of the larger tires).
The ideal (and likely most cost-effective) solution is an aftermarket gear set for the front axle, but this depends on whether or not any are available. If not, then this is where RPO build codes and VINs could come into play. First, you need to know which front axle you have, an AAM or a GM (mine is a GM, RPO=SU5). Then, you need to determine what ratios GM uses (or used) in that front axle. If they used a 3.73 in some truck combination, then you might be able to order GM parts that will accomplish what you need, if the parts are available, and if you can definitively determine the correct part numbers (this is where the VIN from a truck that has the front axle and ratio you need can prove invaluable). From my research back then, it looks like the 3.0 Duramax diesel 4x4 truck was available with 3.73 gearing. What I was never able to determine, though, was which front axle GM uses (or used) in that truck. That's where my own research into a potential OEM 3.73 solution stalled, so I never got to the part about whether these parts are available/backordered/cost/etc.
'22-Limited GMC AT4
Front axle: SU5=GM, SU4=AAM
Rear axle: SU8=GM, SU7=AAM
Do keep us informed of any progress you make. It's probably time for me to resume my own research, too. The 6.2L, 10-spd trans, and tow/haul do a good job of masking the gearing issue with my ~5k trailer, but I can still tell it's not ideal. And even in no-trailer highway cruising scenarios (w/out tow/haul engaged) the slight surge/sluggishness at times is definitely noticeable, as the trans ratios were never designed for an (effectively) 3.08 axle ratio.