Ryan maybe you have never seen how it had been done for years. It is before my time but I have opened up plenty of them.
Twist the solid conductors together (that is the 'other' connection) then solder.
You now have a two connections.
I have pulled these splices out of severely overstuffed boxes, usually a 3" round box, and have never seen one of these go bad.
I think it was Joe T that posted some pictures of how to 'twist' 500 kcmil together before soldering.
I could not find the old instructions but here is a large soldered splice. http://electrical-contractor.net/ubb/Forum4/HTML/000368.html
You gotta love the box fill.