what tech levels are your cags? I'm assuming you upgraded all the relevant techs and have been upgrading the cags with them, which would put them at 41 tech level. Do you have the CAG duty efficiency bonus? Also, looking at your map, it appears to be 'early morning' for where the fight is taking place, and cags suffer in night battles. By the sound of it, the transports have already lost a naval battle and so will likely flee at the first opportunity, which makes me think the fight won't get into daytime.
I too have run into issues with CAGs not performing as I expect, but most of the time I can credit night or weather for the cause. However, I have had several day time battles that make it seem like CAGs only hit the enemy fleet once every 4 hours, instead of several hours in a row and then landing for refuel and rearm.
I've actually made good use of smaller CTFs escorting larger SAGs. The large doom stack fights tend to be much more destructive, though its still a major PITA to kill an enemy carrier. Only real method I've found for that is to blow the rest of the fleet away and then grind the enemy carrier down with a large stack (7) carriers of my own over the course of multiple days, using new cags every time their org runs out. I feel like I'm trying to sink the Bismarck every time I find an enemy carrier.