Your Denali has 3.42 gears and if you want to have about the same effective ratio (a little lower) with 37s run the 4.56s.
You do not need to change carriers in either axle for up to 5.13 gears.
You may want to consider getting the larger rear axle from the RWD Denalis and Escalades, 2007-2013, the 9.5" 14-bolt semi-floater. That can often be had for a song at LKQ. Again, that carrier will handle up to a 5.13 gear.
Remember that those AWD transfer cases demand that the tires be within 1/8 inch in height of each other.
I was going to say there's a gear calculator online. just punch in before and after tire size and it will spit out what gear you need to run to keep the stock ratio..
going rised big tire off road is kinda like going drag racing. it's very expensive if you're not doing it yourself. Maintaining the mods also goes up a lot. as everything wears faster and breaks sooner.
both are fun thou. good luck.