Thanks everyone for the helpful replies. I disassembled the machine the other day, found a parts manual, and started becoming familiar with it. It was a great learning experience. I think the consensus is correct that this might be a leak in the intake hose -- it got better when I topped off my 5-gal bottle, so I guess replacing that intake line would be a good place to start! Further rambling and discussion below, because I just can't leave well enough alone.
shadowfax wrote:I've never heard a rotary pump sucking on a mix of air and water, so it may well sound pretty normal. Easy way to tell is to draw water from the group when it's cold and you know there's no boiling of any kind. If you get lots sputtering then, you know it's from air in the line. Very strange, but I bet air would explain the erratic behavior of your flow meter as well: it relies on a jet of water to spin a little propeller whose rotations it counts. I'm guessing shooting intermittent jets of pressurized air probably makes it a little wonky.
Good point on the rotary pump not necessarily sounding weird -- I was listening for angry cavitation noises but I suppose not hearing noises I've never heard doesn't really tell me anything.

I did notice sputtering (though less violent) when drawing water through the group on a cold machine. So that in my mind at least indicates that this problem isn't caused by a crack in the HX.
shadowfax wrote:The fact that the boiler comes to 1.1 bar and holds that when pulling shots is good, that means you don't have any leaks between the HX and boiler. However, that has nothing to do with an overpressure valve. It's set by the pressurestat. The overpressure valve is on the brew line and should open around 11-13 bars, to relieve pressure from thermal expansion in the HX as it idles and super-heats the water. You'd need a brew pressure gauge to make sure that's operating properly; I have no idea if the S27 sports one of those.
Good point. When I opened up the machine and looked around I realized I had confused the OPV (in the brew line of course) with the boiler safety valve and the release from the three-way group solenoid. All three dump into the drip pan, all three completely different things! At least I'm learning.
One possibility I considered is that there could be a leak in the OPV that was letting air into the line; however, I'd expect to be seeing some other symptom of that, like water from the brew line leaking from the valve, right?
shadowfax wrote:As for water boiling noises, am I right to assume that what you're hearing is the bubbling sound, and not a hiss?
Yeah, I wouldn't take that noise as diagnostic of anything. It just sounds like water boiling. 90% chance is that it is exactly the same as the day it was new and I'm being an espresso hypochondriac.
Thanks so much shadowfax and Heckie for your suggestions. Though this is about the simplest of problems I could have, I'm learning a lot by reasoning through it.