Male cat using kitchen floor as potty :(

[sknash]

I have a 3-year old male ragdoll cat who until a year ago did fine using the litterbox. I should mention he is one of three cats that we have. Beau and Holly are 3-year old ragdolls; KC is a one year old domestic/maine coon mix. Everything was fine until about a year ago when Beau started peeing on the kitchen lineoleum. So took him to the Vet and there were no health issues. At that time I had the Littermaid cat box, the electric one that self cleans. Well, Beau would actually shake if I put him in it to use it. Something must have happened with that particular box, though don't know what it could be. The other two used it fine. So I change litter boxes and get a conventional one, extra large because Beau is a big cat. It is in a corner where there is no traffic & no one to bother them. I still use the same litter, Arm & Hammer for multiple cats. I swear by it. He still uses the kitchen floor. I have tried all the enzyme cleaners to remove the odors. he even pees on the mat where their food is. I just do not know what else to do. The litter box is kept immaculate, cleaned at least 2-3 times a day, once before I go to bed, immediately upon rising. It has to be kept clean for Beau. I am thinking about trying the Cat Attract litter. Anyone use it before? Any suggestions. I have a very small house and am extremely limited as to where I can even place the litter box. They do not go outside. Another suggestion was tranquililzers, but I hate the thought of doing that. I just would like to know why. I would appreciate any help or insight someone can give me on this. I was told one of the reasons he is peeing near their food is because the breeder I adopted them from kept them in cages because she did not want them to get bred with her breeding cats. But why would he start doing it after I have had them almost two years? Thanks for any suggestions or ideas you have. Susan