In a recent game, I was trying to do amphibious invasions against a couple tiny-island cities the AI controlled. These two cities were spaced nicely between me and the long, skinny continent that the AI's main cities were located upon, although I could have bypassed them by going a long way around. The fact that they were located in such a defensive position made me attempt to take them rather than trying to form a beachhead and invade at a different location. In retrospect I should have attempted to buy out a nearby CS, land there, and then launch a navy-supported invasion across the land instead. That way I could have had multiple AA guns to defend the rest of the army. I should also note that I was using Thal's Vanilla Enhanced mod which makes the small islands more useful than automatic razes, but it also doesn't affect air missions as far as I know.
I did also forget that carriers could have escorted my fighters much closer to the invading infantry units.
I had one of the cities bombed down to 1 HP with battleships and destroyers, but I could never get an appropriate land unit close enough to capture it. Even when I had my fighters on the intercept mission and a few squares away from the embarked land unit, every turn that I had an embarked unit a turn from capturing, I'd get a message saying I was bombarded and destroyed by an enemy fighter. What radius does the intercept mission protect? Just the city itself?
Is there any other way to protect embarked land units for an invasion other than send like 6 units all at once and hoping a couple survive to take the city?