Another option it worth to think of and try it, is to include a floating download button, it will remain all the way and it will take action for the screen you swipe to it.
The floating button now became a used behavior even in IOS.
I got inspired by this answer however I object with the placement of the button. In my opinion it should be placed on the right-hand side of the screen, like this:
Why on the right-hand side, one may ask? From the layout I assume the target device is a handheld (smartphone) type.
The facts are that somewhere between 70% and 95% of the humanity is right ...