The Nandina sux but I like everything else! Especially the curvy paths and rock edging.
Against the wall, those Nandinas look like good candidates to be killed by boiling water. I would start @ 1 end and as often as I feel like it, keep heading the other way, pouring lobster pots as safe as full as I can safely carry, right on those suckers until they show no more signs of growing. Cutting @ soil level just before doing it should enable the BW to cause fatal damage to those trunks more easily, more deeply toward and into the roots. I've never tried to kill Nandina in particular this way, but everything I have tried to kill this way is now dead, a pretty good list of plants that had to go. Few plants can survive being heated (or should I say treated) to such a high temp. Just make sure there are no good plants close enough to be affected. Digging a little moat around the crown, &/or using a long screwdriver or dandelion fork to poke as many holes as close to the crown as possible in preparation can also increase the effectiveness.
Then the stumps can be removed, theoretically. Seems like the kind of thing you could convince a strong young person to do for a reasonable amount of dollars, or donuts, ...or plants.
Before doing any of this, call "Call before you dig" if you haven't done that already while there and remember for sure that there's no utilities buried over there. I don't know how any buried utilities react to sudden high heat. Even though somebody obviously dug there before, making the mistake of not calling first in case there's something newer than the Nandinas buried there is too expensive to risk. ...but it would be interesting if anyone recognized, hey, you melted this with boiling water.
