First test: HQ hardness was set to 0.1 x 1000lbs. One 4000lbs bomb (=31 times more damage than necessary!) precisely placed next to the HQ from low altitude. All the guns on HQ blown away, HQ itself still up.
Second test:: HQ set to 0.01x1000lbs (that's 10lbs needed only!). Again dropped 4k bomb right next to it, just a few feet. Nil effect on the HQ itself, only guns and some town buildings blew up. But a few rounds of 0.50 cal brought it down.
So even a bomb 310 times more powerful than needed to kill the HQ had no effect on it. Which proves my initial statement: You need direct hits.