Thanks for uploading the project. I just listened to it and I think I've found the issue.
Yes, the sound is only on the left channel on the click track and is present slightly in the right channel on Output 1-2.
I found the issue by bypassing all plugins on the output channel to see where in the signal chain things were going weird. (This is a good troubleshooting tip ;)
By unbypassing a plugin one at a time I found that on Output 1-2 you had a Direction Mixer with a spread set to 1.5. This essentially blurs the spread slightly... so if you reset it to 1.0 everything should sound as you want it!