I've also been a hiring manager in similar environments and let me give you a bit of advice: don't boast about how strong your filter is. Your best bet at hiring talented engineers is to find great people who slip through the cracks everywhere else.
You're not looking for candidates who could also pass a FAANG process, anyone who could and is applying for your team has something very wrong with them. What you're looking for is that diamond in the rough. That candidate that went to community college instead of Stanford but has built some amazing projects on the side. Or, that person who is not a good fit for big corps and so has left 2-3 of them after a year, might be a bit cranky but is absolutely brilliant and will thrive on the right team with a bit of humanity thrown their way.
My best hires have been candidates that HR threw out.