Inserting a keras layer between two other layers

I have an efficientnet and I would like to insert a custom layer after each pooling layer, right before the ZeroPadding2D layer, and right after the body of the network (before the top).

def cyclify_efficientnet(model):
    model = keras.models.clone_model(model)
    # Cyclization from this paper http://proceedings.mlr.press/v48/dieleman16.pdf
    
    for layer in model.layers:
        # add custom layer 1 after each pooling layer
        if isinstance(layer, keras.layers.GlobalAveragePooling2D):
            prev_input = layer.input
            inserted_layer = CustomLayer()(prev_input)
            layer = layer(inserted_layer)) # Problem: reassignment doesn't change the layer itself
            # layer.input = inserted_layer 
            #??? does not run. Readonly.
        if isinstance(layer, keras.layers.ZeroPadding2D):
            ...

    # new_model = keras.Model(???)
    # return new_model

cyclify_efficientnet(my_model)

In particular, I'm looking at the #Probelm: comment. I would like to do something like this:

input -> layer1 -> layer2 ->layer3 => input -> layer1 -> customlayer -> layer2 ->layer3

But after I get input -> layer1 -> customlayer I don't know how to make layer2 take customlayer as an input while still being connected to layer3 (or more or less the rest of the network). Efficientnet is also nonsequential.

How is this done? I've looked into kerassurgeon but it doesn't seem to do what I'm looking for.