Here's my two cents. Since you are overseeding you don't want the existing grass to grow too fast. New grass roots are tiny, so small that any fertilizer you drop at the seeding time doesn't really do much good for the new grass. So option one is don't fertilize at all. It will keep the existing grass' growth minimal, and you aren't wasting fertilizer. Drop your starter after you mow once or twice. Option two is use a half dose of starter at seeding the other half after the first mowing. Starter is lower in N, so it won't force top growth as much as 31-3-10. The half dose will give some nutrients, but again, the new grass won't be able to use much of the that since the roots are so small. 31-3-10 is too low in P for new grass. Save it for your October feeding.