The layer feed will not cause any serious issues, right away. The kidney problems are from a long term, cumulative effect. With lots of daily treats, a higher protein feed is a much better choice. Just be sure to have crushed oyster shell out for those who need it.
Regarding feed - medicated starter doesn't usually contain any sort of medicine. It usually has a thiamine blocker. And it's such a low dosage, that any that makes it into the eggs is not going to be an issue.
As for something that is safe for all, switch to a grower, flock raiser, or all flock...