Correct, the IQ3 has the 1.33 1NR-FE engine.
Agreed. I've always had coilovers setup professionally (but not always corner-weighted)
The Tein street advance Z look like a good option because they use O.E top mounts. I've found pillowball top mounts to always make the ride noticeably harsher. Spring rates notwithstanding.
As you say, they are very expensive, but I can't see any quality dampers from the likes of Koni, Eibach, Bilstein etc. A quality spring and damper setup would suit the purpose of this car much better.