That is scaryyou need to check out the people who are interested, some will give you a sob story to get the cats then sell them to labs, torture them or use them as snake food or bait to train fighting dogs. Take a copy of their license, get a picture of them and make them sign a contract stating they come back to you in the event they can't keep them. Do not advertise them as "free to good homes" twisted people search for these kinds of ads and pretend to be nice people when they are not. Check out their home where the cats will be, take nothing for granted, check everything out. If they must be rehomed you have to do your very best to make sure they are going to good homes. Once you rehome them follow through with a surprise visit to the home to make sure all is as they said. You can't be to careful, these innocent animals can't protect themselves its up to you to make sure they are safe
Thank youI am glad you asked these questions here. You did a good job calling adoption agencies first.
People who work at veterinary hospitals sometimes foster animals, so if you really can't keep your cats any longer, call them for help. Ask if they have something in the waiting room to post that picture with your name and home phone number on it.
I am sure others will offer suggestions.