Hello Ian,
The car sounds to be a very good buy, and I can understand your views that it must be worth more (a lot more?) than the average 2003 A4 cabriolet.
In my experience, such cars are normally sold to people you know, or people associated with who you know. In other words, it is considered to be a very good value for money car, and someone is prepared to pay a premium for it because it's low mileage and been well cared for.
I once asked a classic car auctioneer to 'value' an 8K Morris 1000 I was selling, and the reply was ' Wharever someone will write you out a check for today, and that will be different to what another person will pay tomorrow!' Not an helpful answer, but a realistic one.
You are the one who knows what you consider it's worth, and this will (as you say) will be based on what is being asked for other average examples. I would be convinced you already have a figure in mind below which you would not sell this car, and if it were mine, I would be tempted to list it online under 'Classic Cars' (which it isn't, but...) and in similar magazines.
If you were going to buy a new car, then no doubt you have already had an unacceptable part exchange price, and this, together with the currently advertised prices of same-year-model cars will allow you to decide what you will accept. Personally, I would not advertised under 'Offers' since buyers will always want to know what you are expecting for it, so just as well ask it, in my book.
Not much of an answer I know, but I'm sure you have a figure in mind, and you might get it from the right buyer.
Good luck in finding the right home.
Kind regards,
Gareth.