Proximity expression whilst maintaining same distance to other comps?

This is a cool challenge!

There may be a more elegant way to do this, but I think this rig setup could be a good starting point.

I thought of this as a chain of layers that you can control with a spacing slider - so you'll need to set it up with a control layer (probably a null) that has a slider effect on it called "spacing".

Then set up your comp so that all the layers in the carousel are in ascending order (or uh, so the next layer is under the previous in the timeline). If you can't get them all in one chunk, just pay attention to how I call the layer index in the below expression.

Apply this to the position property of each layer after the first carousel comp:

var prevComp = thisComp.layer(index-1)       

//change the 1 to whatever increment you need to get to the prev comp's index

var spacing = thisComp.layer("Control").effect("spacing")("Slider") 
var scaleFactor= thisLayer.transform.scale[0]; 

//this will help accounts for how much the width changes based on the scale
var scaleFactorPrev = prevComp.transform.scale[0];

var prevWidth = prevComp.width*(scaleFactorPrev/100);
var prevPosition = prevComp.transform.position[0];
var currentWidth = thisLayer.width*(scaleFactor/100);

var x = (prevPosition+prevWidth/2) + currentWidth/2 + spacing;
var y = value[1];
[x, y]

My main caveat is that you have to pay attention to the first layer's position values if you parent it to a null - and all the position animation to slide all the other layers needs to be done on the first layer or its parent. All the layers kind of pseudo-parented to the layer above them. Hopefully this can trigger an idea! Project file attached.