My dad and I just went through the same process you're going through. He just bought a 2013 128i M-Sport (with me along for the ride). He got the Drive for Team USA credit and put it towards the car. You also might be able to get a credit through the "BMW Ultimate Test Drive" ap. We spent two to three months driving cars and finally ordered a 1-Series.
I think the 128i is an excellent choice. There's a lot of 135 love around here, but I'm with you -- I don't need a car that's "too fast," and stuck with natural aspiration for that reason. Although I last drove a MKVI GTI some time ago, I think these BMW's feel more "substantial" through a turn than a GTI does, that's the best that I can describe it.
I would encourage you not to toss out the 128 just yet. I know it's hard to find one in Sport Package to drive, but I hope that you can find one, new or used, within 100 miles to try. Even if you can't find one in Sport, I think you could get an idea for what it's like by driving a Sport RWD 328 coupe. You'll get a feel for the suspension and the seats, at least. You could then mentally combine that with the power curve and driving experience you felt in the base 128.
My dad just took delivery of his 128i, we've been driving it at length. I have to say how great I think it is. The 128i really shines on a twisty back road, as you're powering through a corner at 3500 rpms and more. It's refined, has comfortable, great seats and a great driving position. It's not fast, but it's really, really satisfying to drive. If I had to critique the car, I would say 1) that I agree with your point about the steering, but I really don't mind it and I think you'll get used to it, I already have; 2) and that I wish the exhaust were a bit louder...I'm on him to get the Performance Exhaust.
Good luck with your search. We also drove a BRZ and an FR-S. We felt that both the interior and the power on those cars were let-downs compared to the 128. He felt the seats and the driving position were far superior in the BMW. They handled well, but that's about it. I'd get the 128i.
PS - My dad's car has the base stereo, and it sounds pretty good to my ears. It's surprisingly close to the Logic 7 in my 330, but has a bit less clarity. Please note that you need to get BMW Assist (+$650) in order to get HK radio.