They won't have poorer throwing range when not fully encumbered. They have equal with their max load. Their throwing range decreases as they got more and more encumbered. Please check my suggestion to make sure we are talking about same thing.
Well, the initial post mentioned "fully equipped (and even over encumbered)" soldiers, which suggested that this also applied to soldiers who are not over their weight limit.
If that's not really the case, then I'm more open to the idea. Still, to be honest, I personally think it's rather superfluous, since overencumbered units are kinda boned anyway. Since they can't move and sometimes can't even use their equipment. But that's another matter.
All these parameters does not have to do anything with weight. My suggestion was to make sure strength doesn't provide "more stuff carrying" benefit and "farther throwing" benefit at the same time. At least not both linearly. They should somehow negate each other. Maybe not completely, maybe just partially.
I can't really follow your logic, sorry. Why would these actions not be limited by overencumbrance, while throwing would be? Can you please explain in more detail?