@Sashajh1   "My fear about doing it that way is that while you can send your passport certified mail to them, they will not send it back to you certified mail."

Certified mail gets the same handling as regular first-class mail, so it is just as likely to get lost.  That's very unlikely, but paying more for certified just makes it easier to figure out where it was lost.  Passports go back and forth in the mail all the time, from people who need visas to consulates that issue them, but you can make your own decision on whether the delay of the EIP is more of a problem than the possible loss of a passport that may expire before the next time you need it.  (I wonder if Social Security will accept an expired passport?)