Does anyone know if there exists a connector that might look like a terminal block except the wire can pass straight through it from one end to the other and the screw clamps down into the middle of the wire to displace the insulation so that it makes a "T-tap" into the wire?
You could spend a little while on Google looking up 'tap' and 'splice' for the wire gauge you're using should find something. I know they make them for various gauge wires. You could probably use a punch down block if the wire gauge was small enough, but they might slice stranded wire, they're meant for solid 24 gauge usually.