I've always held the opinion that as long as there is nothing blatantly contradicting what we already know, then it's not a problem. My own opinion is that the NTF is made entirely of captured ships, there's a possibility that they might have captured a shipyard somewhere in their home systems, but if they did, it was no doubt dedicated to producing smaller ships like fighters and bombers to maintain supply. I expect they would have been very hard pushed to produce even a single cruiser.
As for Hecates, as long as Canon doesn't say that 'Only the GTVA had them', then theres no reason why the NTF didn't, however, even then, you can make excuses like 'Command didn't want to make public the loss of such a new and dangerous ship'.
It IS a game first, and a story second, but with a good story, you can put just about anything in the game that doesn't vastly contradict canon. Ship with 50 beam cannon = Bad, Hecate in the hands of NTF = Meh.