When i fitted my built in fridge freezer i fitted the socket low down under the cabinet behind the plinth. You're not meant to have sockets so low but it was the only option. And there was a gap at the back for heat circulation anyway. The unit has the ability to be turned off for defrosting without turning the socket off so accessing the socket was not an issue though it can be got at if necessary.
In the OPs shoes I'd probably get a 3 metre single socket extension and leave the socket under the unit. Drill a big hole in the bottom shelf if necessary.
In the OPs shoes I'd probably get a 3 metre single socket extension and leave the socket under the unit. Drill a big hole in the bottom shelf if necessary.