Sounds familiar. I have a swath of Lily of the Valley myself, and keep looking at it as if I’m going to dig in, literally, and get it out of where it is growing finally. I’d fork them out in big chunks and divide and transplant the pips, as they are called. It’s a pretty tough plant, so while it won’t love it, probably best to just go for it. I am thinking I will do mine in late summer, since it slows down then anyhow. Key tip: Careful not to hack a lot of roots of your tree in the process. You have to work somewhat gingerly, which is a bit of a challenge with thick mats of a thug like Lily of the Valley. Hence the thought of using a fork instead of a shovel, yes? Best to put it somewhere in a coarser area of its own, like along a roadside bed under trees or shrubs, where it can live alone and not infest and choke out other, gentler souls.