I have an LC-1 *and* a techedge...and oddly enough both work perfectly. Amazing, eh? Maybe because mine was the DIY version...
I call it "use the correct god damn power points".
People will spend hundreds on car parts, but skimp on a few bucks of wiring & connectors. My LC-1 and techedge have received power both from the battery terminals directly, as well as right at the dashboard fuse box from the single-blade accessory slot. I've also used the ground bolt on the t-stat housing to be as "perfect" as possible with zero change. Both log exactly the same via ecu's input as they do via their graphing software (serial data). I've even logged the serial stream of the LC-1 while logging it's WB output wire via an SSI-4, no offset.
All I do is take the single wire for WB output on both and hook it to the ecu's, use good wires, and solder if possible. I don't think my techedge even gets a ground reference via a shunt or ecu, and I have a switch on my LC-1 to use ecu ground or battery ground.