If you have the time you could B-Spec the Dream Car Championship, a convenient 5-race championship which earns you over 1,000,000cr to go and spend. It takes a while (though you could A-Spec it now that I think about it) but the 520,000ish bonus is great because it means you earn twice as much as you would if you grind Indy in the American Championship 5 times.
I do believe though that the rare 21-23 level cars don't stay in the ucd for more than 2-3 races.Sometimes they stay for just one day!A really rare race car,i believe it was the GT one Toyota, was in my ucd,i went for a race to earn the rest of the money i wanted to buy it and when i returned it was gone!
When I purposely reset the UCD I do a variety of things. Do a race, a liscence, a special event, practice, I think that's about it. I try doing different races because I noticed after I did Nurburgring in Dream Car out of the blue it refreshed quite nicely.