I don't have a vehicle or a starter like what you have. Hopefully, someone else can help based on experience.
The reverse-engineering of the protocol shown in the arduino forum does not indicate if it was successful or not. You could try the same approach with just the Electron and not even need the Carloop to do that. Essentially, they were attempting to tie into the serial bus in between the starter module and the remote receiver. The Electron (and most microprocessors) support serial interfaces; it should be quite easy to try that out.
With that approach, if the reverse-engineering is not correct, you could use your Electron wired in the same way to monitor the communications and then you could do your own reverse engineering.
With enough effort, you should have a very good chance of succeeding.