Hi, Sean and all on this post.
I had the same if not a very similar issue with my Zoom H4n and Rode NTG2.
I discovered that the high pitched noise is not present if using the AC plug as the power source.
Previously I was using x2 AA alkaline batteries.
I have not tried lithium batteries with this unit but I do intend to. I will try to report back with any results!
I hope this helps you or someone else faced with this issue.
R