Well written. I have a similar background and I agree with most of your observations and conclusions. Not the part about prestigious universities catering to 'rich kids", though, at least not any STEM departments.
> Why does “as if the waters had but newly retired” mean there’s a lot of water (and thus mud)?
It doesn't. It means there's a lot of mud. It might help if you had the rest of the paragraph in front of you. It sets the scene for us with a bunch of sentence fragments -- bullet points, we would say. Here's the beginning of each of them:
Michaelmas term lately over...
Implacable November weather.
As much mud in the streets as if the waters had but newly retired...
Smoke lowering down from chimney-pots, making a soft black drizzle...
Dogs, undistinguishable in mire.
Horses, scarcely better
... and so on.
And yes, modern audiences aren't attuned to biblical references.
From the parent comment: "Heck invite the regulars to the 2nd drink with that extra money that is coming in now if you want, or give them a discount." That could even be revenue neutral, if she wants it to be. Why not try that?
No, you should always wait until the last possible moment to refill the leaky bucket, because the less water in the bucket, the slower it leaks, due to reduced pressure.