Looks to me like this is to be expected - the enemy has overwhelming air superiority in that region and your fighters have no hope of successfully combating enemy CAS in the air. With this level of disparity, even if you are running pure meta fighter designs against standard AI it is gonna be a hard slog - recommend you switch to interception if not already on it, you may want to just concede the air for now and focus on building up a sizeable fighter force.
On the ground, I'd say things are actually in a better state. Yes you are taking significant CAS damage, but you are shooting down enemy CAS at a phenomenal rate. If you can keep this up, the enemy will run out of CAS in a matter of weeks. You may not be able to push, you may even lose a tile or two, but those losses are not sustainable for the enemy AI.
So I wouldn't be too worried about CAS - I'd focus on winning the air war. Max HMGs or CannonIIs, dual engines, SSFT, armour, extra fuel/drop tanks and maybe a turret and you'll decimate that 4k stack with just a 2k stack of your own. Don't forget to build radar, get better coverage of the air zone with sufficient airfields closer to the centre, finish your doctrine, and maybe even go for motherships if you have them.