To find the cheapest rate, I think you're going to have to shop it around. I assume you have preferred and a corporate rate? Should be a pretty competitive rate. If not, there are some AWD codes on here that you'll be able to try out.

As for upgrades, I was upgraded from an Intermediate to a Camaro SS Conv last Oct in Monterey, CA. I was also offered a C6 over the summer for "just a bit more", but had to turn it down due to company policy... If you're Avis First, you can try renting a full-size and when you arrive request the corvette specifically and offer to pay a bit more.

If you can provide some more details, there are a couple ways that I would recommend going about this. I assume it's still going to be pretty darn cold in CHI when you rent, so you're chances may be favorable.