Elevation will make a lot more sense with PVP. I can imagine the game will play completely different that way.
You could try making the pickup collider a cylinder with a lot of height, so people don't need to get too low to pick weapons up. A larger pickup area in general could be nice. You could also make it so that the weapon that is dropped is not the weapon currently equiped. Since there are three weapons and knowing which weapon gets dropped could be confusing, maybe only allowing two weapons per player could simplify things.
Another option would be to have an inventory system like battle royals do, but maybe that would overcomplicate controls.