Rob,
Looks like it might be best to open a case with GTAC as it will be difficult to fix all your reported issues without switch config or logs.
I will attempt to help. Pull a show tech from the switch and see is anything sticks out. Logs, CPU %, Packets to CPU, STP, L2 protocols, Take packet captures during the ping loss to see if there is a Dup mac or anything odd in the network.
1. With pinging 8.8.8.8 Are you using the ping command with the correct VR?
2. Slow SSH. What is different in that VLAN? Is it a user VLAN? Are there any L1 port flapping or STP transitions. (This Could be anything)
3. packet loss. Probably also the same issue as
#24. Packet captures answer so many questions. Use port mirroring or ACLs with counters to see where the packets are being dropped.
How To: How to create and apply an ACL in EXOS | Extreme Portal (force.com)