Actually I love your stone and I like the setting. But I think I understand. Certain cuts always look a bit different and I think that's why round brilliant is the most popular - it's the easier cut to look good, with princess, emerald cut there are certain angles the diamond looks a bit different.
Just a thought. I wouldn't change the engagement ring. I think it has sentimental value. What I would do is to save for a next ring instead and there you can get what you want!
Not sure I'm helping though...