Bigger is not always better
Don't always try to sell the "big guys." Many smaller companies are involving themselves in sponsorship as they recognize the value of reaching their customers at the grassroots level.
Source: Brandeis C. Hall, RAB
And while the Purinas and Yoplaits are deluged with proposals, those second- and third-tier prospects receive fewer requests for their sponsorship dollars, giving you less competition. Keep in mind, too, that smaller companies can sometimes move faster on a decision to participate.