Instead of .strike(), I believe you might be able to use this long stroke overlay (copy to clipboard from here & paste into your JS code)
Definitely recommend doing your own testing, but this seems to be working well:
Here's some sample code that works for two levels of nesting. It could probably be written more efficiently with more time, but hopefully it helps to get started for your use case 
{{query3.data.map(x=>{x.label=self.checked.includes(x.value)?x.label.split('').join("̶")+"̶":x.label; x.children? x.children.map(y=>{y.label=self.checked.includes(y.value)?y.label.split('').join("̶")+"̶":y.label; y.children? y.children.map(z=>{z.label=self.checked.includes(z.value)?z.label.split('').join("̶")+"̶":z.label }): null}): null; return x})}}
Otherwise, custom css, as Evan noted.