I'm still chewing on this, Pete. <vace> just seems so strange. <vac> seems so much more plausible in spite of the doubling question.  If it were <vace>  wouldn't there likely be at least one word with a soft c in this family?  With <duce> we see both <inductee> and <inducement>, so that seems to make sense. But for <vac> we have words like <vacant> <vacuous>, <vacate> and <vacation> .  Is there perhaps something special about c  that could bolster the candidacy of <vac>? Does c follow the doubling pattern?  I started to investigate cc words and I wonder if they all have assimilated prefixes like <access>  or <succeed> or come from words that already had a cc, (like <buccal> comes from Italian <bucca>  or be loan words like <tobacco>.  I didn't have time to do a full search, but I will later.