Here's what I would suggest... Because I believe we'll *both* find it frustrating to try to communicate about Matthew's toileting across the Atlantic, I think it would make sense for you to get a copy of the book I recommended - as it is very straightforward, predictable, and practical to do. (I believe I mentioned Nathan Arzin's "Toilet Training in Less than a Day.") I have recommended this in my practice and to pediatricians as well.
I believe there's an aspect of Matthew's behavior that suggests he's "got you by the chain" right now... and he's still getting some reward from the reactions of those around him. But, it's impossible to know this with any certainty when you're thousands of miles away.
In the meanwhile, as you're waiting for Azrin's book to arrive, I would initiate (as you suggest) a start chart. Although you'd like to work up to putting stars on for days and weeks in a row, you've got to start off small. Here's what I would suggest.
MATTHEW'S WEE-WEE CHART
O O O
...for every two hours that Matthew either stays dry or goes potty appropriately, he gets to put a smiley face or star on the chart. All charts like this should be displayed prominently (like on the fridge). He should either be the one drawing the smiley face or adhering the star... unless he prefers you do it.
If he gets all three circles filled in - he gets a reward. You all decide what the reward should be in advance... cookie, a special 30-40 minute video, something. He is *not* to receive this reward (or anything similar) during this 6 hour period. No big discussions... if he asks for help in the bathroom, certainly provide it.
If he has an accident, he gets a new chart with three circles. (Essentially, he starts over.)
Once you've had success with this for several days, move on to:
MATTHEW'S BIG BOY WEE WEE CHART
O O O
O O O
This would take care of twelve hours or, I would imagine, most of his day. This time, he needs to collect 6 happy faces/stars across the entire day. The reward remains the same, only the criteria have changed. After several days of success, we then move on to days.
MATTHEW'S BIG BOY DAY-BY-DAY CHART
O O O
Looking for three days in a row of success. (You might want to start at 2 days, depending on his needs.) This then naturally builds until you reach a week or more.
You might need to keep the charts going for awhile, but eventually, you'll need to fade away the reward system gradually. That is, when he's successful, allow this behavior to be the "expected norm" rather than something worthy of celebration. Typically, when a young one is learning this, the "fading away" just happens naturally. Eventually, the chart comes off the fridge, and you have success.
Make sure the rewards are just enough to keep him motivated. Some parents may use a "treasure box" filled with cheap little knick-knacks (balloons (if he can handle them), bouncy balls, whirlligigs, etc.) or cookies in a special jar that are only used for wee-rewards. I don't imagine this would be an issue for you, but I usually reiterate to parents that loving rewards should not be contingent upon his potty-habits. If you always read him books or sing nighty-night songs, don't change this. The message shouldn't be "love is dependent upon your behavior." (Just a caveat - I'm not concerned in your particular case... I just always include that little warning.)
If the charts don't work, and Dr. Arzin's book doesn't help, it might really be time to see a behavioral specialist there in your area. A little visit from "Super-Nanny" in your home might prove far more cost-effective *and* efficient than our e-mail chats.
But, I'm happy to try to help as I can. I hope this has been helpful.