I would put him on the waitlist and see what happens in the meantime. At his 3rd birthday, Charlie didn't look like he was ever going to TT. Then (after some encouragement) he did his first wee in the toilet at 3 years and 1 month. A month later, he was fully TTed.

It happened so quickly once he was ready, that you may find that the same will occur for your son.

So I reckon get on the waitlist first and see how he goes between now and then.