I'm not entirely sure it would be illegal. The ATF makes an exception for parents/children in terms of would-be straw purchases that are considered "gifts." There is technically nothing to suggest that the word "gift" requires that your father must provide all the money for it. Is it a gift if you pay for everything except one penny? Is it not a gift if you father pays for everything except one cent? Such questions are aparently left unanswered by the ATF. After all, the money isn't really what matters: you could go to any gun store in America and give anyone money to buy any gun they wanted, but it doesn't matter as long as they actually make the purchase and take control of the firearm. In your case, your father is allowed to put his name in the little box in your place and assume control of the firearm in your stead (see video). The money is not important, it's who takes control of the gun that matters. And in the case of father/son, even the controler of the gun really doesn't seem to matter much in this case.
There was at least one other straw-purchase thread here where an FFL dealer chimed in and stated that a situation roughly equal to what you have described is legal and is done all the time.