lesser celandine (ranunculus ficaria) please help!

help! i have been cursed by the EVIL lesser celandine!!! (http://en.wikipedia.org/wiki/Lesser_celandine)
i have read that the only way to really get rid of it is with herbicide. is this true? i have quite a bit of it—it has taken over most of my backyard; the majority of the lawn, plus several large flower beds!
the local nurseries only offer synthetic herbicides for this problem. i am desperate enough that i would consider it, but i have pets who use the yard daily, and don't want to injure them, nor any other neighborhood cats who stumble unsuspecting into my yard.
i found an organic herbicide online called "scythe," but can't find it in any local stores. has anyone used it? is it worth paying shipping? from what i understand, it is not only organic, but will kill off the plants you hit with it for good, plus you don't have to quarantine your pets away from the area for too, too long.
besides that, is my only alternative solarizing? i'd rather be able to enjoy my yard not covered in black plastic this summer! plus, i fear they'll just come back next year. those little bulbils are EVIL!
HELP!

Another alternative might be dumping boiling water on them, which will kill them but will also kill everything else flooded with the hot water. But glyphosate doesn't work on celandine? That would surprise me.

i think glyphosate will work on it, but i am just nervous about my pets. the nursery person told me to keep them off it for 1-2 weeks... yowsers.

1-2 weeks is the safest thing to do, but probably not necessary - from what I've read, glyphosate isn't toxic to mammals unless orally ingested:
http://en.wikipedia.org/wiki/Glyphosate#Toxicity
http://en.wikipedia.org/wiki/Roundup#Human_and_mammalian_toxicity