Ok Y., this could've been ME writing this request for help. I am in the exact situation as you - our son just turned 3 this week. And just like your son i think my son too doesn't want to "grow up and be a big boy", nope he's happy being a little boy. when we promised him a big boy bicycle he just brushed it off and said he didn't want it, he was happy with his tricycle.
He has been in underwear on and off for the last 3 months. All the kids his age in his daycare started potty training around the same time as him and they are fully trained now, able to verbalize or even just run to the toilet by themselves without having to inform an adult.
Our son was completely trained 3 months back, he would be telling us every time he had to pee or poop, but all of a sudden within a month he regressed and started peeing and pooping left-right-center in his underwear without a care. So with his careprovider's advice we put him back in diapers for a few weeks and he's now back in underwear. We've tried all the rewards - tattoos, stickers, treats, celebrations ... nothing really had that much impact on him that it made him go to the loo by himself; so i gave up on those methods, waste of my time and effort. I too paid the money and downloaded the e-book "potty training in 3 days", and tried that method, it didn't work for my son. I've read dozens of potty training books including "pt in 1 day", nope didn't work. They all are designed for the initial stages of training where you have to get the child interested in the potty and develop a process; none of them deal with resistant children who know how to pee and poop in the toilet but just choose not to do it !!
Last week i met his pediatrician and discussed the problem that he is not scared of the toilet, when asked to go he does go for the most part, but will not verbalize by himself. And she said the same thing that Alice on this forum has said, that he's almost there, and what i need to do is go back to basics - set a timer for every 40 mins and prepare him abt 5 mins b4 it will go off that "when the timer beeps it's time to go to the toilet, ok?". And make him say "yes, ok'. Or if you have a bell ring it every 40 mins and keep ringing it till he goes, even follow him into the toilet with the bell. I've been doing that now. And also, following his daycare lady's advice, become a little strict abt his privileges. Because i feel that unless he has that push that is meaningful to him, this will not progress. And ofcourse boys will be boys and they are so distracted with toys that anything is a chore. Rewards had no impact on him, so maybe the threat of losing something will. So i keep telling him every 35-40 mins or so that he should tell me or he can just get up and go to the toilet by himself. And inspite of my reminders and timer, if he chooses not to go in the toilet, but does it in his underwear he loses the permission to either watch TV or play with a particular toy, or if he's out playing with friends then i warn him that if he pees or poops in his underweear i will take him home right away and he cannot play with his friends. The important thing is to follow through on your warnings, atleast once or twice, or it will have no effect on him. Same thing before we leave the house i just warn him that he must go to the toilet before we leave, or we're not going; he can cry and fuss, but we don't want any accidents while he's playing, or his friends wont play with him anymore.
He still does not tell us when he has to go, but i think that will happen as something just "clicks" in his brain and he decides that he doesn't need to have control any more. I've seen it happening to his friends, where for months they were in my situation and all of a sudden one day out of the blue started verbalizing. and even when he does start telling you, don't stop reminding him that he has to go or he has to tell you, or else he will lose his privileges. If you stop reminding him, he may just fall back into old ways.
I also have begun believing something that i read somewhere, that some children are not as sensitive down there and their brains /nerves may not be able to sense the urge to pee so promptly, so i try to be patient abt this process thinking my son might just be a little developmentally behind in this area compared to others his age. Just as he is ahead in other aspects.
I'm in the same tunnel as you and hoping to see the light. If you have found something to work for your son, i will delighted if you can share it with me.
-B..