Has anyone else experienced this?

[unfazed]

To fix it (it's worked so far) connect the blue and white wire from the solenoid (starter relay) to the blue and white wire in the brown plug in the wiring junction box under the tank.

What you have done with the above is bypass the starter cut out circuit relay contacts and since it works then, this effectively rules out the starter button and the kill switch as being the problem..

Is the starter cut relay swapped exactly the same as the one on the bike,
Foxeye models use a different starter relay and are not interchangeable.

Check the whitish alarm bypass loop plugs under the seat for corrosion, as one of these plugs/sockets take out the starter circuit.