Regarding the design (all VMKernel ports in the same subnet) and what you mentioned about pinging, I think this might be an issue with the Dell switch - to which vmnic3 is connected - and its uplink to the Cisco switch (VLAN not trunked, Spanning Tree blocking, ...) What you may do is to open a console connection to the ESXi host and run esxtop (press n for networking) to monitor the network/vmnic usage.
André