Helix' Ext Amp switching is transistor based - no relay used.
This kind of topology is called an open collector switch.
Again: The most efficient way to invert the switching is to put it in the firmware - a blind spot on Line 6's side.
I don't know a commercially available device that does exactly what you want.
The next best thing that comes to mind is probably a midi switcher.
If I'd build a device like that it would be based around a transistor (BC547, BC548, 2N2222...) to invert the switching.
Here is what would be needed for one switching channel:
two resistors (R1=10k Ohm pullup, R2=4.7k Ohm base resistor)
a diode or two to protect the transistor
an external power supply input socket
two 1/4" sockets (in and out)
a case
some wire
soldering iron
circuit board (optional)
Disclaimer: I just own a Stomp that has no Ext Amp out. I can't test this on my own.