This is where having a free market again would be helpful. Even if the tests are not so good, people could choose them according to their own judgment. And in the meantime the medical science has an incentive to progress. Someone who comes up with a slightly better test can sell it for a higher price, etc.
Shoot, you can even get a paternity test kit at Walmart for about $25. They're on the bottom shelf near the diabetic testing supplies.