If you have been brave enough to go up to the two wires connecting the woofer, maybe you can look a bit into the internal'amp pcb.
I remember my old Rel Storm3 went mute and was a big ceramic resistor burned inside and at the time this was 'usual' (the resistor just needed to be even bigger smile ).
But what you propose is perfectly fine: the LFE input of your REL is a direct bypass to the sub internal amp (no filters here, they are used with the other inputs like the 'high level speaker ones).
Regards

Basement: Linn Sneaky DS, 568.2mm, ARS Sonum Gran Filarmonia, Ramallo Allegro.
Living Room: 602, Linn Akurate DSM, Hypex Nc400, B&W 802D.