There's an alternative though, which is to do all of your fulltime recruiting in-house, and hire a
software development agency instead of a
recruiting agency to fill the gaps when you're short on employees.
The model of the recruiting agency is that they produce a headcount you're willing to hire, and once you do it they take a finder's fee and are no longer involved.
The model of the software development agency, when you manage them correctly (which is certainly non-trivial), is they produce code which your dev lead approves of via a transparent process which you have approved of, and they have an incentive to get their contract renewed every year. This keeps them honest.
IMO when understaffed, all software companies should contract out their least essential engineering to a well-supervised dev agency rather than rush the hiring process with some dumbo external recruiter. In my experience most of these recruiting agencies have no technical people at all, can't judge the quality of a candidate, and are basically just marketing operations trying to circulate as many resumes as they can.