Some options:
1. Try getting all colours of a certain car.
Here are the colours available.
2. Pick a certain race (I have done this with Seattle and Rome Endurance but any will do). Go down from your normal car and keep going until it is competitive.
What I did was sorted my garage by distance and looked at all of the cars with zero. One of mine was RX8. So I raced that at Rome. I then looked for a slower car with zero milage and tried that.
3. Try picking a car from the pack in the race eg one of the Corvettes or Camaros at the Seattle endurance. Fit hard tires and/or tune up for first race. Then take stuff off the car until you get a close race.
***I just remembered that you said you didn't have the time for a restart. If you don't have time for endurance races then try any of the series and try options 1 and 2 above.
4. Try sticking dirt tires on an unlikely rally car and go rallying eg Vitz, Camaro, 787B.
5. Try the wheelie trick at the test track if you haven't already.
6. Try jumping over cars on the Seattle bumps ie jump over one of the AI cars. I do not know if this is possible but I was experimenting with setups on my F1 cars and almost did it accidentally.
7. Pick a track and try to get your lap times down by fine tuning your setups.
8. Try to find the best setup for 400m and 1000m. What I did in an attempt to find a good Vitz setup was run the 400m on default settings and then went through each setting one at a time. I changed them to min, max and medium and if I found some significant differences then I narrowed it down eg if I ruled out min but not medium or max then I went to 3/4 etc.
I also tried the same with cornering on tracks such as Complex String and Laguna. (still hasn't won me the Vitz championship yet but I actually found it enjoyable).
9. Pick a car (not one of your best or favorites). I tried one of the slow Miatas. Do no upgrades except maybe for tires. See how far you can get through the series it qualifies for.
eg
Beginner
Sunday Cup
Clubman Cup
FR Challenge
Spider Roadster
NA Sports
with this car you probably should skip the GT World Champ (beginner)
and keep going through the Amateur and Pro if you can get the car quick enough.
When you find a hard series try it twice. If you struggle the second time try an upgrade or 2.
Then start the process again with another car.