Okay, I've taken a look at it. First thing, when you open the nif with NifSkope, all nodes that can be seen except for the Light.nif can be deleted (node #75, 77, 78 & 80).
Now to your main problem. This can be fixed easily, it just something I often forget myself until I try the unit the first time. The problem is, that the Rifle_Springfield node isn't a child of the NiMultiTargetTransformController node yet (thats the node you already use for the renaming). All nodes that are child of this node can be modified by the kf files, others cannot. In fact that is more or less a rule of thumb. For example, I forgot to add the Pikeman_weapon node to my infantry, none the less the unit works like it should. But to be sure I would always add the changeable nodes to the NiMultiTargetTransformController node.
Anyhow, if you add the Rifle_Springfield to this node, your unit should work. To do this, click on the NiMultiTargetTransformController node and look at the bottom of the Block Details. There is an entry "Num Extra Targets" and "Extra Targets". As you can see by the green arrow, this is an array. Now to add the node to this list, you normally should raise the "Num Extra Targets" value by one, then refresh the "Extra Targets" array and then unfold it. Now you see the same list of nodes you see in the Block List. Go to the end of that list and you should see an entry with the value none. Replace this none with the number of the Rifle_Springfield node and you are finished.
I said normally at the start of this, because the array already has an empty entry because you deleted on of the pikes earlier. So you can skip the raising of the entry "Num Extra Targets" this time.