You actually want plenty of head space when fermenting mead in the primary because you will be adding nutrients and degassing, which causes a volcano of sorts. Then in secondary you do not want head space. Rack into the gallon jars and make sure that the mead is all the way up into the neck. I would make 3 1/2 gallons to account for the trub you will want to leave behind.
So primary and secondary does matter with regards to head sppace and oxygen tolerance. Primary=oxygen good, lots of headspace; secondary (essentially bulk ageing)=oxygen bad, very little headspace.