Put the earth-peat mix in before the water and mix it around evenly. Then add your sand layer (make sure you wash it first) on top of that. Once you do this, you can place a small bowl or plate on the sand to spread out the flow of water, when you add it. Go slowly if you're using a bucket and try to disturb as little sand as possible.
If you're planting, say, a stem plant like Rotala, the sand should keep the stems in place if you push them 1-1.5" into the substrate. For rosette plants, make a small 'crater' in the sand and sort of 'scoop' the plant into the sand. Keep the crown above the sand. After that, you can push some sand around the roots to keep it in place, kinda like a newly planted tree.
Depending on the root systems of your plants (ex: Echinodorus vs Rotala), it may be slightly tedious to uproot them. If you have an exacto knife, you could try cutting around the plant to sever some deeper roots before you pull up. Whatever you do, pull slowly and gently, allowing for the substrate material to sift back into place. Some dirt will come up but patience will minimize this. Done properly, you shouldn't have too much mixing between the layers.