What options do I have to speed up s3 modtime HEAD request?

It can do, for instance in a sync that will be controlled by --checkers.

However for a mount I don't think it does issue them in parallel unless the application using the mount issues the stat calls in parallel which it probably wont.

s3 will support whatever you can throw at it - it is amazingly robust! Amazon will charge you for each of those HEAD requests, but they'll work fine.