If you've done a quote with 2 older named drivers, you're probably within about 20% of your lowest possible price tbh. It's possible to haggle them down if you've got a second company with a not-far-off quote, but you'll only get so much off with that.
The area you live makes a massive difference - I live in a category B area, with relatively low car crime and accident rates, and mine is about £1,000 at 22 on a new A3 170TDI BE. If I put in a Bradford/Salford postcode, I get £8,000+ or just plain "no quote available"... the area makes a huge difference. Age seems to make a difference, sometimes moreso than NCB - although obviously the two often come hand in hand, so it's hard to compare sometimes. £1000 is a fair chunk of cash, but I just figure it in with my fuel costs (another £1600 or so a year, I think, with 10k miles [10000miles / 45mpg * 4.5 litres/gallon * 1.6 £/litre]) and then add general tyres/servicing/cleaning products/bulbs and other expenses on top.
I've not tried with an S3, I might run a quote through out of curiosity sometime - I don't do enough driving on the right kinds of roads for the S3, so an 170TDI has plenty of power for my needs and I get to save a few quid on fuel.
Does it have to be an S3, or could you live with a 2.0T S-Line/Black Edition? If so, try some quotes with that. Also, stick in a lower risk postcode (LA1 4DX if you want to try one I happen to know is pretty low-risk) and see how that comes out. If it's about the same, there's not a lot you can do. If it's significantly lower, it's your location being the problem.
