When you say 'online agency', do you just mean ones in your area that have a website to advertise? Most seem to have an application form for you to fill in and submit, or at least an email address for you to send your details to (and you're quite right not to send face pics) which sounds like exactly what you've been doing.

If you're determined to employ an agency for whatever reason, I can only say keep trying - if you've had no response so far then the ones you've tried don't want to represent you (and are bloody rude to boot for not at least contacting you with a thanks but no thanks, so you're well shot of them) and it'll be a matter of finding one that does. Or going independent and hanging on to your earnings.