I'm really sorry to hear you're having such problems. The agency just sounds like they're being really vindictive, so unnecessary after your ds has been with them for so long, you would have thought they would want to leave on good terms and remain friendly especially if he is lucky enough to go on and become really successful, he won't remember them kindly now

Such a shame, people move agencies all the time for various reasons, most adult agencies are done on a "handshake" agreement with no need to put in any penalty clauses, the relationship should always be friendly and beneficial to both parties.
I think it's to your advantage that your ds is still a minor (under 18). It is very hard in contract law to enforce a contract with a minor, whether or not the parent has signed on their behalf.
For example:
“...a contract with a minor is voidable. That means the minor is able to cancel any contract at any time before reaching the age of 18 and for a reasonable period after that time. There is no requirement for the minor to have a justifiable reason for this, it can be done on a whim or where it may be advantageous to the child to do so."
"A court would not "force" any person (whether it be an adult or minor) to carry out a contract for personal services because as a matter of public policy, parties should not be forced to continue in a personal relationship against their will."
Even where the parent signed it on the minor's behalf (is the contract in the parent or the child’s name?), if it’s in the child’s name there have been cases in court where the judge has said that a parent cannot be held responsible automatically for the contract of a minor because that defeats the fundamental proposition that a minor cannot be bound.
So you could get your ds to terminate the contract himself - he could send a letter with "Without Prejudice" at the top (in case it goes to court) and cite the following case:
"I draw your attention to the case of Proform Sports Management Ltd v Proactive Sports Management Ltd [2006] EWHC 2903 where the High Court considered a contract that Wayne Rooney had entered with his agent and this was found to be voidable on the basis that it was not necessary to permit Rooney to earn a living. Instead the contract was seen to be a “trading contract” even though the contract added value to, and facilitated Rooney’s career. The contract was therefore voidable at Rooney’s option."
The “Without Prejudice” at the top is in case they decide to take you to court. However there really is no chance they would have any success in a small claims court now for any “breach of contract” claim for damages, as they have refused to accept the very generous and advantageous early termination agreement offered by you and your new agent, and this would go against them in court proceedings.
Basically they are the ones behaving really badly, having a signed contract does not allow them to act against the best interests of a minor who is protected by law.