"Tricking" ethernet cable it's disconnected
Frame challenge, you're starting from a wrong premise:


  Physically disconnecting the ethernet cable is the only way of turning
  of the ethernet port on the FPGA, which consumes a pretty large amount
  of power.


is not true. If you know you would be fine disconnecting the cable, you can also:


force the core into reset 
stop clocking the core using clock gating
Countless other things, depending on how you implemented/copied the ethernet core


Messing with the Physical layer of the signals should be your last resort. Being forced to take this route shouts that you messed up your earlier design decisions and are better off going back to solve these.

As mentioned by Peufeu: if your PHY is a separate controller, just reset this. I assumed it wasn't, but it's not completely clear from your diagram that it necessarily isn't.