In the digital world uppercase letters are like shouting so whilst they are much easier to read (depending on the font used) having lots of text in uppercase is a bit like having a room full of people shouting to get your attention.
I can see your logic and it is sound insofar as readability but in this instance it detracts from the app, making it hard to focus on just one area because there are things in uppercase lower down the page that are vying for your attention.
There are a couple of things to do that would make your buttons and headings easy to use on the go:
1) Use a symbol or icon next to the text on the button so the user just has to look at the symbol rather than read the text.
This app uses symbols to allow people to categories at a glance.
2) Colour co-ordinate the buttons so that each activity has it's own colour (this can be tricky, especially if you have lots of buttons) so the user only has to look for the yellow (for example) button.
This app has coloured the buttons different colours to make it quick to identify
3) Use small caps to make readability easier whilst avoiding the problem of "shouting"
To avoid legibility problems choosing a font from the Sans serif (both examples I've used have sans serif fonts) or a serif font (like Times New Roman) should combat a lot of issues. For a collection of easily legible fonts on mobile try these:
Free Easy To Read Fonts for Mobile - Sans Serif
Free Easy to Read Fonts for Mobile - Serif
I collected them myself and they all have licenses which allow for use in an app.
However, I would go for both symbols and colours and keep the text capitalised (This Text Is Capitalised, it means making each new word start with a capital letter and can be confused with uppercase). This doesn't detract focus and can, if done right, give you a very visually striking UI.