AFAIK there is no easy way to do this. All model coordinates are global so you can't place your labels with relative coordinates which might help in this case. In my experience scale also causes the model to move in 3D space as it scales relative to the 0,0,0, so if this is off to the side of your part the part will translate away from 0,0,0 as scale increases. Here are my suggestions on possible solutions:
1. Switch to a fixed scale increase and use a toggle button to switch between scale = 1 and scale = x. Then you can either make two sets of labels (one for each scale in the correct position) and hide/show as needed, this could be done all without code. Or you can change the coordinates for the label position to move one set of labels, this would require some JS code.
2. Write a bunch of JS code to take the slider value and apply a transformation to the 3D label coordinates to move them thru space as needed to maintain position. This would give you the the nice slider scaling action you want but would be a lot of math and work.
