Nice diagram. That is exactly how I attack a phalanx.

I also put my secondary troops (like velites or what have you, but high-attack flankers work best) in the center and my heavy legionaries on the flanks. I make my center stand in front of their center and not attack, and just attack their flanks.

If they turn to face the flanks, they will expose a new flank to your center. If they do not turn, they will be systematically cut down by your flanking attack with heavier infantry. Either way they cannot maintain a solid phalanx line against you, and you won't have to suffer undue casualties trying to hold their line when you can hold their line without actually engaging (if you throw javelins at them their center will come forward, making your flanking maneuver even more effective). Most of the time the AI just stands there and gets slaughtered.

I think Publius Scipio did that to Hannibal Barca's brother around Massilia and it worked pretty well.