I had similar issues with my progressive lenses, so at my last appointment, I asked to get two pairs of glasses - one with normal far vision and another pair of reading glasses for up close. (I also had the need to use up $1000 in a flexible spending account that could only be used for vision and dental - my son didn't get braces this year, like I thought he would!). I thought this would be a lot better. I could see all my monitors in focus with my normal glasses, and only when I want to read a book would I switch to my reading glasses. My optomitrist recommened against my choice, but I did it, anyway.
While I am happy with my new normal pair of glasses when working on the computer, I am frustrated when using my phone (the iPhone 6 Plus, so it's not a tiny screen). I find myself moving my phone farther away to be able to read it. This happens to me all the time, so it gets very annoying. I think a better choice would have been a pair of progressive lenses for every day use and a separate pair for just the distance to the computer screens, and I'd leave those at work. If I only had the budget for a single pair, I'd go back to the progressive lenses.