I see your approach. And Cretan archers are good for that long distance archery fire. I love playing the Greeks myself. It's a pity their cavalry is of only modest quality. One can compensate for that by building the Temple of Nike series so that you can get some extra experience chevrons to boost their effectiveness. I like building the Nike series temples @ Sparta, Syracuse, Tarentum and Thessalonica myself. That way, when I recruit my Spartans at Syracuse and Sparta, they're always going to have the extra experience chevrons.

The dogs are definitely annoying to Greek cavalry. Your cavalry will always vanquish the dogs inevitably, but not without taking a few casualties.

The harder the difficulty level you play the less time the AI will allow the factions it manages to just sit under archery fire. When I first started playing the game on 'easy' setting, to learn the ropes, I could get in fairly close with my army and have my archers rain down death while the enemy just stood there. But that happens less often when you play at the higher difficulty levels. Still, long distance archers are a must-have. And if you can maneuver your army in such a manner so as to neutralize some of the elevation advantage that the enemy might have over me, it's worth the extra marching. Missile troops are hugely more effective shooting downhill than uphill (which only makes sense.) And . . . the dogs have to move uphill at you. They, too, are less effective fighting uphill. Heavy peltasts would definitely be a good choice for those operations you're describing. Of course, 'heavies' aren't recruitable until you've built your catapault range. And if you've built that, you can recruit onagers which can really rain death down from a distance. :)

I'm a bit surpised that you're able to split your force the way you're describing without suffering too much in consequence. One of the things the AI loves to do is the suicide charge. If it sees a nice vulnerable unit like peltasts exposed, the AI will charge cavalry straight at them. I guess if you give your missile troops close escort support it discourages that behavior. Still, the AI behaves strangely (by our human standards) and will charge single units of infantry at your cavalry units. The AI seems to benefit the more chaos it creates on the battlefield by spreading you out. But you seem to have a handle on things.

Good hunting! Especially for the dogs. :)