If you personally want to check your password wouldn't it help to curl more queries? Probably also taking care to make not too much per some unit of time?
Even with 10 or 100 queries you still will get a probability distribution of (I'm guessing) 20-200 passwords that make up the most likely 50% of passwords, so I'm not sure how much good this would do if your password is relatively common. If it's very obscure this could help more, but you're still narrowing the password search space from 500M to 5k-50k.
Yes, if you suspect your password is common maybe you shouldn‘t use that service at all, but just download some smaller list of “common passwords.”
I also see problematic that, if I understood correctly, some browsers query automatically that service with your passwords which browser collected whenever you “saved” some login.
If you personally want to check your password wouldn't it help to curl more queries? Probably also taking care to make not too much per some unit of time?