The only time I'm in a rush and don't check on Google or another concordancer
Didn't even know there were 60m signed balls in existence...
Have to say though that I'm happy with both "signed" and "autographed" in all the contexts we've mentioned. An either/or example possibly, with differences in frequency ("signed" seems to win hands down) but with both remaining possible and dependent on idiolect -ie the tendencies of the individual speaker? It may be that "autographed" is more usual amongst older speakers ( like me I'm afraid
) - but that the language is changing to favour "signed"? User age is unfortunately something the concordancers don't tell us. A pity, because it has enormous relevance...