Hey, D.. Here is what worked for our twin boys also at age three. We knew they were ready, because they were beginning to play games with us..."can I have a toy?" or "I'm mad Mommy" and poop under the table. We tried everything as well and nothing worked, untill this:
Our pediatrician told us to - LET them go in their underwear. I know, gross! Then, make HIM clean up his mess of cleaning underwear in the tub, starting a load of laundry, washing the floor or wall or toilet or whatever is messed from it, wash his hands and have him pick out new underwear and pants. Of course you'll have to help, but make him do the majority of it.
The key to this (and it's hard to do!) is to stay completely calm and act like it's just a fact of life that when you mess, you have to clean up. Rather than making a fuss about it, we said "well, guess you'll have to clean up again. But don't worry big guy, you can try to make it to the potty next time. I beleive in you!". It's hard when you have pee or poo everywhere and seemingly endless cleanup, but well worth it.
Our boys both went through this procedure only twice each and even began to sleep through the night in underwear! We were psyched. Good luck to you and your big boy.