Getting them to potty is like all the other biological functions we teach them. There isn't anything magical about it. Stop rewarding him, stop making it behavioral, and let it just be biological.
With that said, he is old enough for his diapers to be taken away. This literally means no pull-ups, no diapers, pee and poop goes in the potty. Clean up the messes without saying anything negative, and he will get it real quick that pee and poop go in the potty. Just put aside a few days, put him in trainers and give him the chance to learn timing. If he can go on the potty, he is half way there, he has control, now you need to give him the chance to learn timing. Usually it's best if you let going potty be their idea.
Also, don't do the timer thing. Literally just talk to him about the sensations and pressures when he has accidents and direct him to the bathroom. Give him quick, no fun showers, and he will quickly get that pee and poop go in the potty.
But do institute "rules" after he is close to being trained. 2 and 3 year old are very distracted, so they do need help sometimes. In our house, for instance, everyone goes potty before going outside to play or before leaving the house to go somewhere --including mommy. We have little bathroom outings. We do the same before meals, and I let them decide if they need to go.
And do yourself a big favor, once he is mostly daily trained, put him in cloth diapers at night. Yes, I said cloth diapers. It will help him quickly decide to learn night control. Big pees are very unpleasant in cloth diapers ;-) Both of my kids decided to start using the potty in the middle of the night (at 22 months) thanks to cloth diapers.