I would agree, they are pretty extreme options. I suppose it depends on how much you need those apps to be installed and stay up to date. It's certainly a weird problem, one I've never run across before, which is why I only have limited suggestions.
A root app ... the best way to describe "root" in general is that it's the difference between being a building's tenant or its superintendent. With root, you have keys to everything on your tablet, but you can also cause a lot of damage if you don't know what you're doing. Root apps usually will do things your phone can't/won't do normally, everything from changing your boot animation, backing up your apps, and deleting systems apps, to completely revising your Android experience.
For me, I got into rooting by researching it and following directions. It's not that hard if you follow things to the letter (and have some patience and spare time).
For a casual user, I'd say it's too big a gun to bother with.
Just one other thought, have you tried accessing the Play Store on your computer and seeing what the app install status is there? Sometimes you can order the computer to send the app to your phone.
--I do a good impression of myself--