Hey, designer. I know screen real estate on mobile is extremely limited. I know it would be really nice to fill the whole screen with content and just have a little, square, "more" icon tucked in the corner. I know you've tried to establish the hamburger icon as the universal "more" icon.
Too bad. Users aren't catching on as quickly as you'd like. They don't notice, understand or utilize the icon. Even if they do notice and understand, an ambiguous "more" is dramatically less engaging than explicitly showing what they can get. A "more" icon is asking them to expend effort up front exploring your interface with no clear reward in sight. So, they don't bother. Like, a measurable 50+% drop in engagement don't bother.
So, stick to tab bars as much as you can. It seems like a waste of screen space. But, the results still seem worth the cost.