Thoughts:
1. Most of the time, if the ICE is running, then it's geared to the wheels, at least the way that I drive (mostly freeway). I base this on watching for the little white "gear" indicator...
Then, the motor turns about 30mph per 1,000rpm (see my thread on using DashCommand). So, unless you're setting the cruise at 130mph, the ICE is not turning 4,500rpm.
2. When the ICE is generating electricity, then it tops out at ≈4,600rpm (at least in "normal" mode).
NB: that's with the pedal to the metal, and only briefly, at the high end before the fake shifts lower the rpm again. (It does NOT run at a constant 4,500rpm!)
I'd guess that otherwise the ICE is running 1,500 to 2,500rpm in normal driving.
(I need to drive around watching the tachometer in DashCommand some more.)
3. My understanding is that knock is a bigger problem at low and mid-range rpm, not at high rpm — quite simply, at low rpm there's more time between ignition and TDC, and at high rpm there's very little time between ignition and TDC.
So, it's quite possible that the HAH is retarding the ignition of the ICE at low RPM to prevent knock.
4. The price premium for premium gasoline here in California is typically only 30¢, which is ≈6%. (I just filled up with 91 octane for $4.75/gallon.) I'm skeptical whether 91 octane will yield 6% more mileage, but it might be close...
I suppose the amount of time the ICE is directly connected to the wheels depends on your commute. I don't do much freeway driving so I'm mostly in EV-ish mode. My commute is mostly surface streets, with maybe a 1-2 miles out of 10ish total where I can see the gear occasionally. On the highway, though, you should be seeing the gear most of the time.
In retrospect, I tried to simplify things a bit too much. I picked 4500 RPM as an upper limit because I've seen some efficiency plots of similar Atkinson cycle engines, and they all fall off a cliff around that RPM. It doesn't make any sense to run above that in a car tuned for efficiency. In reality, it likely has to pick an RPM less than that if there's no reason to spin the generator and/or wheels that fast.
You are correct, knock can happen anytime. In a modern production car (not tuned by someone that doesn't know what they are doing), it is hard to cause knock unless you are giving it a lot of thottle, which I was equating to driving hard, which equaled high RPM in my head. However, that is not true, and most ECUs monitor knock at low and medium RPM (I have a turbo Subaru, and it actually ignores the knock sensor at high RPM because the engine is not the smoothest and will cause false knock). You can try to induce knock at just about any RPM by mashing the gas pedal to the floor while being in too high of a gear at the time. This loads the crap out of the engine, doesn't allow the engine to rev, and allows the intake manifold to shove all the air into the cylinders it can. If you have marginal gasoline, this is your best chance at causing detonation (please don't actually try this...). What I don't know is if this is even possible to do with this drivetrain - the throttle is electronic, so the ECU could (in theory) prevent this scenario from ever occurring.
Again, I think the 91 octane recommendation is targeted towards the 1.5T because it can generate very high cylinder pressures. The 1.5T has a 10.6:1 compression ratio and a turbo that can push 20psi of boost. This implies cylinder pressures of (20+15)*10.6=371psi at the end of the compression stroke. The 2.0 hybrid is running 13.9:1 compression at atmospheric pressure, so 15*13.9=209psi, which is overstating things because of the Atkinson cycle intake valve timing. So, the smaller turbo engine is seeing peak pressures that are nearly 2x what the hybrid is producing. If you compare the torque output of the two engines, the smaller engine is producing nearly double the amount of torque per liter of displacement, so the cylinder pressure math checks out. With that said, I read somewhere that the hybrid engine runs at stoichiometric air/fuel ratio for a wide range of conditions, whereas turbo engines often times inject extra fuel under boost which helps keep things cooler. This could cause the hybrid engine cylinder temperatures to run a little hotter than the turbo. Still, it can't be running exceptionally hotter, otherwise it would start failing NOx emissions I would imagine.
I have a OBD-II scanner somewhere but I have not tried to connect it to this car. I wonder if it can read knock counts. That's really the only way to conclusively answer this, but I don't really drive enough to burn through reasonable quantities of gasoline to do A/B testing of various octanes. If it does knock on 87, I would be surprised, but who knows.
Around here, premium is something like $0.60 more per gallon (I think, it might be even more). I think it is possible to get better mileage using premium, but there is no guarantee.