I would think the best thing you could do would be to provide good clean water and a stress free environment. An airstone might help get more oxygen into the water, gasping is usually due to lack of oxygen. In an uncycled hospital tank you may need to change some water daily until you start seeing an improvement.
There is no way to tell if your fish can recover or if too much damage has been done. Since it has been struggling for over a week now, it may be “too little, too late” to help this fish.
What can help your existing fish would be to get a proper test kit which includes ammonia, nitrate and nitite at the very least.
Also, your tank is really only suitable for 4 or 5 adult angels. You should find a new home for 4 of your fish, or see if the fish store can take them back.
I’m not sure what happened, but you seem like a well-meaning fish keeper and you were probably trying to stay on top of your water changes. It is possible you had a crash in your aquarium which caused your tank to go through another cycle. If you weren’t on top of regular water changes in your extremely overpopulated aquarium, then perhaps it was a spike in ammonia or nitrite. To prevent unstable water parameters in the future it is important to be able to monitor water quality and without the proper test kits that is not possible.
Good luck. I do hope your angelfish recovers, but just know that it is possible he has sustained too much damage.