The problem with Liberate Country is the 100 Warscore required for liberating Australia means I would have to fight a war solely for Australia, and I would have to project both naval and land power from the USA across the Pacific and occupy every province there to get the Ticking Warscore required to win the war.
Free Country, on the other hand, has a far lower Warscore, and if UK is suing for peace from badly losing a war for Canada, I can "tack on" releasing New South Wales. Using Place in the Sun for New South Wales, releasing Australia, choosing "Play As", then consoling back to USA, incurs next to no net infamy. Either way, with POPs of Darkness mod I can follow that up with Free Allied Cores to give Australia the rest of its cores, although the net Infamy would be significantly higher than if I just used Liberate Country from the start -- I would prefer Australia to do the dirty work of actually adding Wargoals for their cores and occupying the provinces themselves.