Do not have time to read the entire thread now, but wanted to add something that seems significant to me.
The kid has more interest in approaching the challenge if it is shared with intellectual peers.
Seems that my kid is much more interested then. Take today - He has been invited to the meeting of an ARML club. He kind of felt obligated to attend, since the e-mail came personally to him. We said - go to this one meeting, see how you like it and then make your decision. He muttered something about "chores" on Saturday but went. Came back all happy , saying he is going to attend regularly. Why? He already knows 7 out of 14 people from a different math club, they are all smarter than him and he wants to rise to the challenge, he wants to be able to contribute (I think that they solve problems as a team there).
