I guess, narrowing in is more efficient than brainstorming. Facts beat speculations.
In deed it sounds more like a phaser. As I see there is no active effect in the signal chain. I have no idea, how the PROFILER could be the origin of that issue.
Headphones connected to the PROFILER would be an easy test.
You could start at the HEADPHONE OUTPUT then try
Have you exchanged cables and guitar?
Have you tried to connect any other powered monitoring equipment instead of the Headrush?
What if you fed your smart phone into the Aux in of your PROFILER?
How is the Headrush connected and is this the only monitoring equipment connected?
Could it be that you have two XLR cables connected from the MAIN OUTPUT of the PROFILER to the two inputs of the Headrush and mixing those in the Headrush?