You don't necessarily have to specialize based on the size of the screen. You could have one fixed pixel size that works on the average device (say an iPhone, since they all have the same screen), and dock the panels to the various corners of the screen.
As the screen gets bigger, the controls stay the same size and in the same relative place, simply showing more screen in the gaps that grow.
That's great, and that's exactly how it works right now.
The problem, my friend, is that this method doesn't really work. A typical 7" tablet runs at 1024x600 and a typical 10.1" tablet (over 3" bigger!) runs at a mere 1280x800, not enough to compensate for the 3" increase in screen size. The UI elements have to be completely reworked for a bigger screen that isn't running a much higher resolution - unless they can be scaled by the dimensions of the screen, which, like I said, is impossible, since the DisplayMetrics API is completely unreliable.
After about 720p you're probably in tablet country, so you might as well permanently unship the menu.
For smaller devices, you'd need to make the bottom bar scrollable but that shouldn't be too hard.
Contrary to what you say, this is both important and worth it, because I would not give you money for the app looking like it does on my device.
Even knowing how good an app it is, how dedicated the developer is, I still wouldn't. If I had bought it, I'd use the refund button and since it's free I wouldn't buy any of the DLC, simply because it's very ugly and fairly unusable.
Users are picky, and if you don't give them perfection straight away they will throw you in the trash and forget about you.
Alright. I'm sorry you don't like it. Maybe you'll like it in an update!
Edit: I did make a small improvement, but that's all I can do for the moment. Hopefully when it comes out you'll give it a download, and if you still don't like it, oh well, can't please everyone :/