I think they've ran us very smart. There's no spiraling debt like there was with the administrations before. We're not tied-to a sugar daddy who, if ever left would leave us in massive trouble. If Chelsea, or City, or Newcastle owners just randomly stopped funding them, they would crash and burn before stabilizing. Being managed properly, we may not win as many trophies today, but the club isn't at risk of dropping out of the Premier League the moment a sugar-daddy gets tired and stops funding us. (the aforementioned clubs would have to have fire-sales to balance the books).
You said it yourself- we went from £300mil to £5bill worth. The clubs finances are bringing in a lot more money now, we've grown, we can afford more and still balance. Don't forget, a lot of our money is going into stadium investment- more long term financial planning rather than short-term gains.
You're right, they got lucky with Klopp. We wouldn't have won the Premier League with any other manager. Unfortunately, I also think he's a victim of his own success- our salary bills are higher now, we're less nimble in the transfer market. As Carragher says, he's got too much control and taken away some areas from the specialists.
Klopp is the blessing that won us... well, everything! He's also a bit of a mill-stone in some ways too, he's no longer accountable for mistakes because of his past success. Not a Klopp-bash, there's no other manager I'd pick before him, just acknowledging that there's downsides to Kaiser Klopp just as there are upsides.
As for whether we are in serious **** if Klopp leaves or not... I think that depends on who takes over. Our financial stability means we won't crash and burn... but we probably won't win anything for a while either.
We're stable under FSG and that to me is a good thing.