And the nasty part of this trap? If someone does start mimicking you, but with a clean new UI, and your market share starts to slip, so you say "fuck it, I'm gonna do it that way too", then you will force your users to make a choice.
Stay, and have to relearn the whole website, or leave, and have to relearn the whole website.
I feel like one thing I've learned the hard way is there is such a thing as getting successful too soon. Once people start voting with their feet or wallets on your solution, you're stuck with it. "We'll fix it later"? "Later" is gone, kids. There is no "later" anymore, we have what we have. If you don't like it it's time to start on a new project.
could you not incrementally improve the UI, without a drastic surgery of the UI? For example, add an extra screen here or there, add theming support, then allow UI customization, then, add a new IU selectable as a new theme, etc etc.
If you chose the wrong abstraction for the project, it's often reflected in the logical structure of the app and it takes some serious creativity to correct it without changing the UI very much, IME.
Often the things that make the app hard to work on also make it hard to use.
Couldn't you incrementally introduce those changes? Sneak in the major overhaul in frequent, minor ways?
This is what happens to me occasionally with my web app. The design is the same for 5 years now. I'm tired of it, it clearly has limitations, but users are very happy and new users compliment me on the "clean and great design". I really have to fight the urge to make a major redesign and rewrite huge chunks of the code base, because it wouldn't solve any problems users have.