Port mirroring across multiple switches?

Hello,

I currently have a network setup like this:

The target state is to be able to sniff any device from "Switch Home" on the "Monitoring PC" plugged into "Switch Core".

I have it working, though I think it's creating a lot of noise on my network by mirroring all traffic on each switch to the next one in the chain. I am not using VLANs and don't quite understand how to use them or if they can help here.

Three switches

Switch Home - Computers to be monitored are connected here
Switch Work - Switch between Home and Core
Switch Core - Monitoring box is connected here

The switches will not directly forward packets from the source boxes' ports via the uplink to the next switch.
You must select an EMPTY switch port on that switch and forward it to the uplink port to the next switch.

Currently setup like the following:

1. On the Switch Home, computers to monitor are on ports 2, 11, 12, 13, 14, 15. Uplink port from Home to Work is port 1.
2. Configure Switch Home to mirror port 3 (unused) to port 1 (Switch Work).
3. On the Switch Work, port 1 is the connection from Switch Home. Port 8 is the uplink to Switch Core.
4. Configure Switch Work to mirror port 6 (unused) to port 8 (Switch Core).
5. On the Switch Core, port 8 is the connection from Switch Work. Port 8 is the monitor box box.
6. Configure Switch Core to mirror port 8 (Switch Work) to port 1 (monitor box).