The DTD price will be inclusive of the £3k deposit contribution e.g. if there's a £4k total discount, £1k will be out of the dealers margin.
I have used DTD a few times before, they put you in touch with a supplying dealer to take your order (its usually the fleet sales side of things) and they get a lump sum "finders fee" from the dealership when the purchase is complete.
If you are impatient, you can see how many S3s are "in stock" on the Audi.co.uk website. They will all be built, some will be sat at Emden waiting for a ship, some might already be at the dealers. They'll have various options. If you can look around the named "in stock" cars and find one with the options and colour you want, you could be waiting as little as a fortnight for it. This is what I did. I would guess though that the cars in stock right now won't be the black edition, as they've not long started building them. I got £4760 total discount, including the deposit contribution, just by asking.