You get a lot of advise. All of them are right.
I think you can not afford to stop working there.So you must organize all around you as much and as fast as possible.
1. get some tambourine and use it when you want to get attention of all the kids.
2.describe to the kids that all of them must look at you if they hear the tambourine sound and then do what you ask them to do.
3.you can ask them whatever you want: jump 2 times or say woof or clap or ....
4. when kids just BEGIN getting loud get all their attention by the tambourine and say "low (indoor) voice". In your situation it is most important thing you must get under your control.
5. stop trying to get them sitting on a rug and entertain them by some activities. It doesn't work in your situation and with your age group of kids.
6. organize a few activity centers and keep kids in group of 3-4 kids in each of them. (coloring/lego/bloks/fine motor skills/cars/dolls/reading.... ) You rotate kids from center to center. Do not allow them to leave a center without cleaning after themselves.
7. set your own place by the entrance and keep 2-3 kids near you with some activities. You can read to them, or let them to play with some puzzle ... it can be anything that does not take too much of your attention.
8.make two box "school" and "home" and cards with kids names. When kid leave (s)he must find own name and move the card from the "school" box to the "home box". You can start your shift by little art activity: they can decorate own name card by using stickers or color them or ... (just be creative)
9.choose some of kids as your helper. S(he) should remind to kids to move a name card from one box to the other. It will slow them down and help you to see who is leaving.
10 count kids!
11 Use low voice.

In Russia I used to work as an elementary school teacher. 25-30 6yo kids and one teacher. No problem.
In public daycare centers are 25-30 kids for one teacher and one teacher assistance.

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