That was kinda my thought too, and I never went to the track this year.
Not sure how well you can see it. In back of the tires (sitting in cups) is a bar. I plan to cut the bar and weld the strap into them. At first I thought it would be best to put the strap under, but the way this pivots makes that impossible. Most trailers do have something sticking up to cup the tire, so it'll stay.
On the winch. You may want to aim for larger than 3,000lbs. 97 Bonneville weighs ~3,600lbs, then adding on some resistance to pulling it up the ramp, the winch may struggle. I've brought a come along with me before and luckily never had to use it.
No matter what, you'll love it and it will also have you browsing Craigslist for 3800 cars under $500 that need something easy and can be flipped for good profit.