Your router doesn’t handle LAN traffic so an upgrade shouldn’t make any difference, unless you have multiple VLANs and are passing traffic between them and don’t have a Layer 3 switch in use to handle inter-VLAN routing.
I would probably start with an iperf test for download bandwidth to the Pi from the server. If that looks OK then I would benchmark the NFS share for read speed on the Pi, make sure that’s not doing something weird.
If that all looks good then I would probably suspect that Kodi either isn’t using hardware acceleration properly, or the specific media codec is not supported by the Pi for hardware acceleration.