By your description of the sound, "clicking", I would suspect CV. Bearings, easily checked by 12:00 and 6:00 position on tire and check for any play, of course tire is off the ground.
U-joints make all kinds of noise as well, but that "clicking" sound, I hate it.
Have someone walk beside the truck while you drive and see if they can't help isolate the area that is clicking.
I have had Ujtns transfer sound through the hubs, sneaky trucks, where someone had to lay on the ground as I drove slowy past to help pinpoint the origin of the sound.
Very interesting idea about swapping sides, are you sure it was not a Ujnt like domestics use for final drive? Knowing a CV is simply a cage containing some large round bearings balls, can't see reverse rotation having any effect, but that is just my lack of engineering knowledge.
I say yank'em, inspect'em and expect to replace'em.
Got a bone-yard close by, could be cheaper alternative than brand-new.