I think having the tab header at the bottom looks nice, but on the other hand, it also looks out of place with other headers like in Clock or Settings, which are at the top. I was thinking whether you could make it possible to swipe from the normal to the private tabs like in Clock or Settings, but then it’d become more frustrating to swipe back to the web page you were reading.
Perhaps we’re all looking at this the wrong way, and tabs shouldn’t be on a completely separate page in the first place. For those who can install Android applications, it’s worth taking a look at Firefox for Android. I think they’ve (finally) managed to create a well thought-out design that’s reasonably intuitive, doesn’t require a hundred taps to get to where you want to go, and just works™ - all it needs is a more swipable interface that doesn’t require two-handed usage. Clearly, OMP has already looked closely at some aspects of Firefox’s design, because the new menu pop-up is eerily similar in both looks and functionality.