By the time I have built up a large enough stack to wipe an AI (done in the most efficient way possible) they've already got defenders capable of defending the rush.
This might be one problem. You don't need a stack large enough to wipe out an AI before declaring. You only need enough units for first target, which could be one or two cities. As long as you have reinforcements coming in, you don't need any more units than those that will immediately see battle. Strike sooner, aim for important cities first, then you cripple their research and they won't reach tech for counter unit in time.
Some other things:
-Super medic obligatory. Use promotions for healing and plan your healing to avoid wasting turns on that.
-You don't always need healing to full strength. A 10.8 strength cuir is just as good at mopping up severely wounded units as a full strength cuir. A 0.2 strength catapult bombards city defenses just as good as a full strength pult.
-Using later Great Generals for promotions in the field is mostly better than settling them on normal speed. You need to build 10 units with settled GG for same XP gain you get in the field. But in the field you get to use this XP immediately and you can target it on the units that need it the most.
-Don't be afraid of losses. Sometimes you have really bad odds on top defender, but attacking immediately can still be better than waiting for stronger units or bombarding one more turn.
-Keep your army busy. A unit doing nothing while waiting for reinforcements is a wasted unit. Look for opportunities to pillage, capture workers, kill stray units out in the open and lure tough defenders out of cities. Or just scout the next city instead of passively doing nothing.
-The AI is capable of more stupid things than you can imagine. Be ready to take advantage when this happens. Typical example would be fear of whips. Some players would assume the AI always whips another unit when you approach a city and not move in before they have enough units to handle this extra defender. This is not at all true. The AI might instead whip a worker or settler for you to grab. Or they might move out an existing defender. I've even seen the AI move a galley into their threatened capital and loading some defenders onto the galley right before my attack.
-As already mentioned by others whip whip and whip more. You need the army fast.
Btw. This thread belongs in regular Strategy&tips, not the strategy articles subforum.