I´m not sure I agree the HQ getting attacked constitutes a defense, albeit weak, of a province that would be attacked anyway. Quite often a province stands empty for a long time, after I´ve removed the defenders. Then by some chance, the HQ arrives literally 3 hours ahead of three panzer divisions, and at that very moment, one of the neighboring divisions attacks and routs the HQ. It´s obvious they attack with the goal of doing just that, not an effort at the province. In literally no time, the enemy from a province on the other side of a huge city say, gets knowledge of an HQ entering, attacks it, and sends it packing, right before the main force arrives and kicks their behind.
I guess there´s no real solution to this now, so I´ll just live with it. The easy answer would be, as mentioned, to be able to attach the HQ to a fighting division, and move with them. In real life, different parts of a large combat unit doesn´t get magically teleported to the next province, separating the unit.