I used to race personal watercraft professionally and this is what I learned from dealing with potential sponsors:
1. Make sure you emphasize what you are prepared to do for the sponsor. Don't go talking to sponsors and say "Hey you should sponsor me and give me free goodies". Tell them what you intend to do for them that will attract potential future customers to their product.
2. Your idea of allowing them to install product is great. But make sure you also emphasize that you are willing to let them use your car for future advertising, promotional gatherings, car shows, etc.
3. Tell the companies that you are their representative (literally) and that you know how important it is to them that their image and your's portray's the company at all times. So don't get caught street racing where your car appears plastered all over the newspaper, etc. Sometimes bad advertising can be good though. But don't drive like an idiot when the companies logo or "Sponsored by" sticker is plastered on your car.
4. Ask the potential sponsor if they have any ideas to help market their product better than it already is. Just show that you are more concerned with helping the sponsor rather than what they will do for you.
5. Plaster everything with their logos and offer to help the company handout flyers (at car shows), answer any questions about their product to future customers, etc. Also keep the car clean at all times when its on display.
6. Contact future sponsors using a resume. And on your cover letter emphasize everything about you and the points I have raised above.
7. Lastly....try not to ask directly for over the top requests. Let the sponsor detrmine what he/she is willing to do for you in return for what you offer up. If they don't get to that point highlight to them again what your willing to do for them and then politely ask what you can get to help them market their product.
8. My mother advised me to keep my mouth shut at races and don't swear around kids who look up to you. Just try an maintain a friendly stance and the sponsors love it when fans, etc can talk to the person who owns the ride. People who get this kind of access to yourself usually listen and go and buy the sponsors product right away.
I may sound like a know it all (I don't mean to) but I kept my sponsors (Jetpilot, Smith Googles, Bombardier Seadoo) very happy and they in turn paid for my entry fee's, gave me tons of free product, and gave me deals on product that normally only employees get.
Good luck!
pro5.