What you're trying to do seems very similar to this game's character: Little Slime Blows Up. The creator of the video talks about the technique used there.

Essentially you distribute circular rigidbodies in a circle and connect them all with spring joints (desired distance based on circle positions).

It's almost the same as a regular softbody, but implementing it yourself will allow you to tweak it until it matches your desired behaviour.

To overcome the intersection problem mentioned, you could add a Polygon2D collider based on the poisitions. Just make sure to disable collisions between it and the outer circles.