I'm 100% serious about that. Around here, we will take a barrel, cut it in half so that we have a steel tube to contain the fire, then we will set the stump on fire and burn it out for good. Depending on where you live, you may not be able to do that (it also depends on how dry the surrounding ground is. You don't want a wildfire), but it works for us.
Depending on how close the hostas are to it, you may have to transplant them, or just plant new ones. (BTW I'm not good at keeping plants alive, but I can sure kill the hell out of them.
You may want to get a second opinion about the hostas.