My concerns come from players interacting with each other simultaneously. The host of the game will process turns in the order his or her computer receives them. That means players that click first get to act first. There was one instance where I was able to "snipe" a barbarian camp from another player. He had dealt most of the damage on previous turns, but I managed to click first to get the last hit, giving me the free gold.

Yeah that sounds... problematic. Why not do it like Laser Squad Nemesis or that one WW2 game (I forget the name) and just queue orders for your units and cities, and then everyone carries them out ALL AT ONCE but without any control. One obstacle in that approach might be having to program a "rules of engagement" AI system for your troops if they encounter opposing forces, but it's definitely better than lowest-ping-gets-first-strike approach cluster-eff implementation here.

Or just do a traditional take-your-turn sequentially. At least, that's how I played my Civ4 games with a couple friends.