I really do not understand how anyone can sign the photo unless they know you, as they will be saying it’s a true likeness of you (but for that they must know who you are)
If the consulate says in effect anyone can sign the photo, why not ask them if they will do it ?
It all a bit ridiculous, as if you were renewing a passport and your appearance has not changed that much then the photo does not need signing. In your case you are applying to replace a lost passport but Passport have a copy of your photo on file, so why should they want a copy signed. Red tape !!!
As a police officer, I signed my wife's application a few years ago. I included a letter explaining that as she had been on my passport and we were married I was the best person to say the info was correct. My colleagues thought the application would fail but they sent the new passport.
You could try sending your application and explain that you cannot get it signed, as no one who fulfils the criteria is available. (They must be a British citizen so in theory your bank manager in Spain etc cannot do it)