I have had this enrichment problem all along, at least for some of the enrichments. I set my global vertical settings to disabled long ago when I asked about this long ago (and just checked to see if they're still correct, which they are), but the problem has persisted for me through all the updates.
One thing to try -- which may just be a placebo effect -- is to go into terrain and paint it as rock, and then lower both your brush size and brush intensity in the terrain menu to the lowest amount. (and then make sure those settings get saved before opening the enrichment item tab). Again, this may just be a placebo, but I feel like for some of the items (not necessarily all), this has sometimes helped to at least decrease the amount of terrain impact they have. (You can of course go back and repaint the terrain the way you want it after you've placed the items!)
I've also noticed that as I move from biome to biome in different zoos, it feels like I notice the problem more often in some biomes than others. I'm not sure if this is biome specific exactly, or if it has to do with the heights or the basic soil types that underlie each biome. Or even if it's just that I'm keeping different animals in different zoos (and thus using different enrichment items). Or just that I'm starting from a flatter surface more often in some biomes than in others.