So last night I jacked up the truck and checked pretty much all of the suspension and steering components, I found a little play in my tie rod assembly, but nothing too concerning considering you'd be able to manually turn the wheels a bit even with just one side off the ground. What I did find, however, is that my front driver's side tire (305/40R22) had a large, clearly visible bulge in it. I swapped the F and R wheels and took her for a spin and violá, significant drop in the felt wobble in the steering wheel and front end. I could see the rear wheel sort of "bouncing" at low speeds when the bulged section strikes the ground out of the side mirror, so I'm fairly confident that I'll be fine ordering a new tire (maybe 2 for good measure?).
I'm not going to change the thread title to "SOLVED!" until I get the new tire on and verify there are not other issues, but for now I'm still considering going with new shocks like
@swathdiver suggested.