As for the 'noise' factor, try red-teaming your hiring processes, though for your particular situation it may not be the best. For example: with the major job sites, make a fake profile that is a 100% match, apply for your jobs, see if the fake person gets through, at what rate, etc. Do it for 90%, 80%, 70% matches too (define the % match as you see fit).

Trying to 'hack/red-team' your own system may reveal weaknesses and flaws you weren't thinking of and help the hiring process. See what penetrates, what doesn't, chat about it over lunch, etc. And yes, it does seem like taking an adversarial approach towards your very own hiring processes is insane, but here we are.