You'd also need a really transparent oil to avoid path length differences changing the colour of the objects. As it is the reflections that appear further out are dimmer because of mirror losses, and it's these that would be affected most. We now have such oils, but they have a cost, and they're not traditional so there's little incentive to use them. In a kaleidoscope stored on end, the objects would sink in a thick layer of oil, and not redistribute very well.
But a layer with a bit of thickness might work, as the eye has a certain depth of field in which items are fairly well focussed. This depth of field is greater in bright light, as the pupil contracts. So you can have a thicker layer of objects with brighter illumination. But it would still be a fairly small fraction of the distance from the eye to the objects.
However depth perception is largely from binocular vision, which a normal single-eye kaleidoscope lacks. With only one eye, depth perception comes from expectations of the size of familiar objects (not applicable here), seing what is in front of what, and loss of focus. So the effect wouldn't be as interesting as you think.