What I'm trying to do is change my character's weapon. It never changes, and I'm not getting any errors related to the unit, nor the weapon.

I changed the "WeaponName" to "WeaponName1" in the ODF, and put this in my script when an objective is completed: Both the class and the weapon do exist and work.

You do know that the unit in question has to enter and exit a cp (usually done through respawning) for the change to take effect, right?

Uh, no, I didn't. *is embarrassed*
Well, that... changes things. I don't suppose there's a way around it, like killing and respawning in under a second? Or changing the ordnance, rate of fire and geometry of the gun?

Create a CP that you can enter from far away (not sure about that, maybe properties in ZE or the odf), place one and give it a unique name, kill it upon mission start, and when you want to change someone's weapon, respawn the cp, force them into it like you would into a vehicle, force them out as you would a vehicle, and kill the cp. I think that ought to work. Not sure if you can treat CPs as vehicles, though.