How to handle 4 wires using 3-port AlumiConn connectors?
You have two options here

You have two options here.  Either you can daisy-chain AlumiConns as you describe, using 12AWG copper THHN for the jumper wire, or you can use a single Al/Cu rated mechanical tap connector (often called "Polaris connector") rated for the wire sizes in question (the smallest size you'll find can take anywhere from 14 to 4 AWG), provided the latter will fit into the box.  An ILSCO PBTS-4-4, for instance, takes up about 2" by 1.3" by 1.4" (LxWxH) and requires a torque setting of 20 in-lbs for 14-10AWG wire.  Either way, you'll need to torque these connections correctly, as you are already doing with your existing AlumiConns.