Well, I think I have a work-around. It's not what I had hoped, but it will do the job. I wanted the profile to work so I would not have to split the app, thus raising issues with shared variables.
But, I need to share the variables, so I have tried writing a single digit to a file and then reading it back, splitting to get just the single digit as a variable again. This works, but it takes time. These e-readers are not the fastest devices on the block.
The purpose of the variable is to identify the type of book and, therefore, the reading app to open when either the bookcover image or the open book icon in the status bar is tapped. It finally penetrated my thick skull that the second app could do this busy-work in the background, based on whether the first app has closed or not. This is a trick I have used before on this device. That way, when the icon is tapped the variable is already known and it's either choice 1, 2, or 3. Done!