Removing/killing Fuchsia Magellanica

I have two long-established and neglected FMs that I need to either dig out or kill. I can't use a conventional fork, so I imagine I'll have to use chemicals on them. What's best to use? Root Out? I've cut one down but not the other; the stems are big enough to drill some holes to put the crystals in, then cover them with polythene. Would that be o.k? Is there a better way?

I'm clearing the garden and won't be replanting this year so a quick solution isn't necessary.

Thanks!