For a car model, you really want the paint to be fully cured before you polish. I've found that there are a few choices in this situation:
1. You can build/use a drying booth as mentioned. I don't have one, but I have put the model under a 'light' with a light fan blowing air across it. Seemed to work OK with the Humbol enamel I was using (my experience is that Humbrol enamels are about the slowest to dry/cure that I've used.)
2. Change paint (although it sounds like you've already done some painting). Using a lacquer paint will decrease drying time significantly. Some rattle can paints are enamel, and some are lacquer. Pay attention to the label, or do a 'net search on the brand name and you'll likely be able to find out exactly what kind of paint it is.
3. Let the paint dry on it's own. If you've got 3 weeks, that should be good. Do as much pre-assembly as you can. The only thing I think you'd really need to wait for 'cure' time is the car body. Assemble as much else as you can, then finish it off when the paint is cure.
Good luck, and hopefully we'll see some pics over here too!!
Murray