Now, I'm not there, but I certainly hope that this inspector is basiclly wrong. I'm wondering if it's possible that he took too negative of a view of the hive, which has gotten you now in a panic state. Try and think of all the "facts" and find what's actually "true" with the hive. Did YOU think the hive was getting really small before the inspector came by?
I'd also like to say that it is possible it got smaller, but that maybe that's just fine and normal. After all, most hives pretty much "shut-down" by the begining of September. They may still fly, and they'll still work some, but probably won't build any more wax. And the fact that the hive was strong a month or so ago, but now smaller, makes sense really. If the queen laid eggs like crazy in the summer, and those eggs hatch - then you have lots of bees. But then 1-2 months later, the queen slows way down in laying eggs, AND the mass of bees hatched 1-2 months ago DIE...... well, the hive gets smaller. Add in the fact that the younger bees in there may not be collecting any of the sugar water you gave them, but instead doing clean-up jobs within the hive like young bees do.
I don't know..... like I said, I'm not there to see the hive in person, but it sounds like a normal fall hive - bees dieing off, less larvae laid, less foragers - majority young bees. Some of the stuff the inspector told you are probably (or ARE) right - such as having an old queen, and she would be less of a layer. Just don't panic yet. Slow down and look at each aspect of the hive - how old are the bees, how full is the hive really (of bees and honey)...........and so what if they don't have enough honey for the whole winter, just give them a warm place and feed them.
Do like we all do - do all you can for them to be warm for your climate (windbreak? tar paper?), lessen the space in the hive (take off un-needed supers), feed them, and PRAY. :) There's certainly nothing wrong with finding a nuc, but is it really needed? I guess if I was there I'd look you right in the face, reach two feet up and stretch my arms out as wide as possible to grab you firmly by your shoulders, smile, and say "you can do it, you can get these girls through the winter".