A question for the experienced gardeners here...

A guy hired me to do some weeding around his rental properties. They are older homes, and there is a lot of liriope growing around the foundations. Unfortunately, there's also a lot of weeds, including vines of all sorts and tree seedlings. In my own experience, I've found that it's virtually impossible to pull weeds in an established (i.e. thick) liriope bed because it's so difficult to get things up by the roots. Sure, I can cut back the trees, but they will sprout right back (I don't necessarily need the job security that this situation would provide).

My question is: would it be worth it to start over? In other words, I'm thinking of removing and saving a few weed-free sections of liriope, cutting everything back to the ground, spraying with round-up repeated times over the course of several weeks, then tilling everything under. Then I would replant small bits of liriope, mulch, and watch it fill back in over the next two years or so. As long as things are kept mulched and weeded, it would still be a great aesthetic improvement, even in the short-term.

Has anyone tried this before, or would anyone recommend it?