Hi, ceiling_fan (nice name BTW) and welcome to GTPlanet.
My times were like this, on T2s with no pit stops, and no qualifying:
Deep Forest:
Total: 14':54.503"
Fast Lap: 1':26.671"
Margin: +19.007", TRD Celica
Rome:
Total: 16':52.915"
Fast Lap: 1':38.254"
Margin: +33.605", TRD Celica
Monaco:
Total: 19':10.138"
Fast Lap: 1':52.699"
Margin: +31.355", TRD Celica
From looking at my notes I realized I had the race LSD set at 10/30/20 as well.
The key here, particularly at Monaco (and to some extent Rome) is to carry as much momentum as you can into the turns, and be gentler on the throttle at exit. Otherwise the front end washes out and you hit the wall, which alwyas costs time and speed. I've also done it in a 197hp Lupo Cup car (NA1, I/E1, chip; otherwise stock) on T5s with somewhat similar results but a little smaller margin. That is a fun little car, too.
If I can offer any specific advice let me know. Otherwise, try the Xsara rally car if you need to get the job done. Good luck!