I can understand why they don't touch the top of the screen: the tab stacking shows up above the tab. My suggestion would be to expand the tab to the top of the window, and then just make the tab stacking show up inside at the top of the tab. If not that, at least make the tab's bounding box touch the edge of the screen and leave the tab stacking on top of it.
I found a few more issues while typing this up: 1. The browser seemed to think my CTRL key was stuck or something. Typing in my password on imgur made it switch tabs and zoom out multiple times when I went to type some of the numbers in my password. 2. Copying the image URL from the address bar after I uploaded it didn't copy the protocol. The protocol was hidden since it's http, but that adds an extra step of typing "http://" when I wanted to paste it here.
The browser looks like it has promise. I like the look-and-feel. I like that the address bar is the progress bar when the page is loading. Being able to add notes and screenshots also seems like it would be incredibly useful.
Overall, I'd give the browser another shot once you've made some more progress.