S3 and Type-R is a ridiculous comparison. They don't compete with each other at all. Apart from being of similar size and power, that's it.
The S3 is specifically targetted at people who want accessible performance with the surefootedness of all-wheel drive in a luxury package. The Type-R is the ultimate evolution of the archetypal "hot hatch", totally focused on performance and handling at the expense of everything else and with extreme styling to match (personally I think it looks like it's been 'styled' by an eight-year-old). The BMW attempts to bridge the gap by blending the performance/handling focus of dedicated hot hatches like the Type-R with prestige and luxury.
It sounds to me like the Type-R is more what you're looking for which begs the question of why you bought the S3 in the first place as it patently wasn't what you were looking for
Sometimes you cant predict how well a car will fit into your driving/lifestyle in the future. Sometimes we make the wrong purchases in life.... worse problems to be had for sure!
......also the latest Type R was only a flick of a designers pencil, when I ordered my S3.
The last shape Type R had loads of issues too.
But the magazines are going crazy for the latest series... would be nice to own a car the fits My persona .......... unlike the 50+ Midlife somethings that usually end up in The Mad hatches. Trying to reclaim lost youth for when they owned a Mk3 capri back in the day ......