Debug slow lan (ssh, nfs) file transfer
Solution 1:
At the numbers you get, seems like something is not actually gigabit in your network.
Use ethtool or something similar to check the speed on each machine NIC.
Check the switch and make sure the ports are actually active at gigabit speed (check LEDs or configuration port status if the switch supports management).
Run iperf or an alternate between the clients.
Finally, check CPU usage - perhaps something is wrong there.