OP chose the option of cancelling his DE segment and rebooking himself. He is entitled to a refund of the value of the unused DE segment in addition to the delay/cancellation compensation of EUR 600. He may also be entitled to some "duty of care" compensation, but it appears that he was on his way soon enough so this may all be minimal.
Air carriers really have no reason to make it easy for consumers. Recent studies suggest that only 2% of eligible claims are even made and there are largely no consequences to the carriers for not paying, beyond the brand damage and administrative hassle.
DE could have issued the EUR 600 on the spot to OP's bank account and the value of the ticket segment as soon as the rate desk could run it and the duty of care via a voucher. But, why?
DE won't be particularly the worse for the wear after OP files his claim and as to the many other pax on the flight who likely never file a claim and are happy with an extra night at a hotel which DE purchases in bulk for a pittance, there is no downside.