Thank you for the reply. It is very helpful. I was considering the change of the coil to a thicker one, but if we are talking about extreme subtlety and not about removing a bad/not intended characteristic, because of the cheaper part, I will thrice consider the change. First because of the cost of the new coil, second space in the speaker for the XO (convenience) and third the speakers are not that fancy or other of my hifi components, that could benefit from the change. But when the mood strikes you, who knows.
Of course I am changing the coil in the woofer and the capacitor in the tweeter and the resistors in the direct path to the speakers. I was just wondering about that coil in the high pass.