Frontier can set whoever they like as the controlling faction of the ship in its new system (and indeed secondary factions, for more variety in mission offers). If they do add multiple factions to the destination, possibly someone could put one of them in charge instead.A Megaship is being sent to aid the war effort, but by whom? Who's going to control it when it turns up? Who's going to be handing out the missions?
It'd probably make most sense to have it be labelled as AXI - plenty of (non-player-submitted) CGs have been administered by PMFs recently who just happened to control the relevant station - rather than giving it back to Merope Expeditionary Fleet, but either would work from a plot perspective. It's AXI the Pleiades-focused NPC group, not AXI the players, who'd be in control in-universe.
(If it did go back to MEF, such is the risk PMFs take on when capturing plot-relevant assets or systems)