I'm also hypothesizing that based on my high head pressure relative to relatively low flow rate that any fluctuation in output from the pump could be exaggerated in water height.It could possibly be that theses variable flow dc pumps are inconsistent with their output.
I was just about to type that as i finished reading your post.
Personally i never had a bean animal drain, i ran a herbie drain for years with a ac pump and a ATO , never an issue.
With that said it seems consistently high or low. It will drop an inch over the course of minutes sometimes (I sit by this tank all day in my office hence the reason it drives me extra mad), I'll go bump the pump up one or two percent, and it will quiet down and go back up an inch in a matter of a minute or so, then a few hours later it will be heavily flowing over the drain making that noise and I have to go bump it back down a percent or two and again it's fine.