PaulS:
Is there a way to use pulseIn with another timer than the one used by the interrupts?
pulseIn() doesn't use a timer. It waits for the state to change or for millis() to have advance far enough. Since millis() doesn't advance when you have interrupts disabled, it's hard to believe that disabling interrupts allows pulseIn() to work. Not hard, actually. Impossible. Unless the thing that enables pulseIn() to return is that the signal actually changes.
Turning interrupts off disables servo pulses, so it's no surprise that the servo doesn't move.
So, why are you turning interrupts off?
Turning interrupts off and then on actually helped for the PulseIn function. My input was clear, with no oscillations.