About artillery, i always find they fire the first salvo exactly 5 minutes into the turn, so far so good. I very seldom let the AI plan artillery strikes on its own, because there is a delay, and I like to use my arty where i want, when i want. When I plan the strikes, i see when they will be carried out and choose my targets accordingly. The best setup i've found is to point at hexes when i'm almost sure the enemy WILL be at the time of the strike. For example, if there are three enemy units in a row rolling down a street, i'll plan my first strike against the middle one, plan the second strike an hex ahead, and then somewhere else because by the time the third strikes arrive,they will probably be too far to accurately predict their position.
Moving units it's sometimes tricky and I concur sometimes moving times don't seem to follow any reasonable logic, but it may just be a combination of a dozen different factors. Unit quality, enemies near, c&c blunders, enemy comm interference, etc.
The asyncronous command cycle, however, i don't think allows for a rapid response. I feel it's just a realism mechanism, and i'd say Flashpoint Campaigns shows you how POORLY accurate orders from "higher ups" can be on a battlefield. You issue your orders, and by the time the unit receives them and act on them, they may not be accurate or relevant or even useful anymore.