Have you considered setting up stations around the room with different activities? They'll be able to move around even with the fixed desks and be able to look forward to the next activity.

Here is a way to separate them into groups:
You can do things that are different than just numbering off or calling out names that are time savers as well.

Prepare index cards ahead of time with different numbers, colors, shapes, words, etc. on them. Hand one to each student as they enter the classroom at the beginning of class. If you'll want your students to get into more than one group during a specific class period, you can even use two (or more) different types of classifiers on each card. Then, when you want the students to get into groups, just tell them that you want them to find the others with the same color or same word, etc. (You can still use a reward for the first group to get together, if you want.)

Your stations can all coincide with whatever unit you are doing and can consist of games, active reading activities, problem solving, etc. Check out the website below for some great ideas on games.

Now, as for the noise level, you can also use strategies such as having the class whispering while playing rather than talking to keep the overall noise down.

Using teams is crucial to class discipline while playing a game. Anyone misbehaving or talking outside of the context of the game means their team has a point deducted. That has worked really well for me.

Kind regards,
Shelley
Receive free games and ideas to make teaching children more fun on: www.teachingenglishgames.com