So here's the point I was trying to make: AC 120-76B on page 4 paragraph d says:
Portable COTS-based computers, considered to be PEDs with no FAA design, production, or installation approval for the device and its internal components. Class 2 EFBs are typically mounted. They must be capable of being easily removed from or attached to their mounts by flightcrew personnel. Class 2 EFBs can be temporarily connected to an existing aircraft power supply for battery recharging. They may connect to aircraft power, data ports (wired or wireless), or installed antennas, provided those connections are installed in accordance with AC 20-173. (Portable Class 2 EFB components are not considered to be part of aircraft type design; i.e., not in the aircraft TC or STC.)
Therefore it should be perfectly legal to connect your PED to an existing antenna that is currently not in use. Since there are a lot of old DME antenna's on aircraft, and the frequency band for ADSB-in is the same as the old DME signal, I would suggest leaving the DME antenna there and someday use it with your stratus.