Save The Dates

I would probably still stay in the 6-8 months range. I think for father's day most people don't make their plans until a few weeks before. Maybe just do 8 months so you're still in that range, but just a little earlier.

I would send them out around October-November if it was me. I don't think too many people travel for fathers day

I agree that you don't need to send them out earlier than usual for that particular holiday weekend because that's not really known as a traveling holiday. But I do think it's good to remember that sending your save the dates out earlier doesn't guarantee anything about your attendance rate anyway. People will still make their usual plans, or not, and likely decide whether or not to attend your wedding when they receive your invitation.