Fixes #9571, various other tweaks.

code/game/objects/structures/stool_bed_chair_nest/bed.dm

@@ -32,6 +32,9 @@
 		padding_material = get_material_by_name(new_padding_material)
 	update_icon()
 
+/obj/structure/bed/padded/New(var/newloc)
+	..(newloc,"steel","cotton")
+
 // Reuse the cache/code from stools, todo maybe unify.
 /obj/structure/bed/update_icon()
 	// Prep icon.

code/game/objects/structures/stool_bed_chair_nest/chairs.dm

@@ -44,6 +44,7 @@
 		var/cache_key = "[base_icon]-armrest-[padding_material.name]"
 		if(isnull(stool_cache[cache_key]))
 			var/image/I = image(icon, "[base_icon]_armrest")
+			I.layer = MOB_LAYER + 0.1
 			I.color = padding_material.icon_colour
 			stool_cache[cache_key] = I
 		overlays |= stool_cache[cache_key]