Electrical – Does a common neutral between solar inverter and utility affect current measurement

I don't have experience with the specific models you are referencing but I do have experience with phase locking AC power sources. The bicycle analogy above is exactly how mechanical generators work and with solid state power inverters to the point of the inverter "pushing" on the grid however you don't want the grid to ever "push" on your inverter. The inverter watches the 60hz sine wave from the grid connection to trigger the driver to keep the output in phase with grid power. This is going to be a high impedance detection circuit so any source should do the job such as your pure wave inverter off a car battery. The listed tolerance on the sine wave is well outside the normal tolerance for mains. How precise is the frequency of the AC electricity network?

While connected to the grid it is critical the inverter is synced to the grid frequency and phase as tight as possible to prevent the inverter from seeing the grid as a load. If the grid were to have just gone down and your system started automatically the phase could be 90deg out of sync when the grid power is restored which would be worse than shorting the output of your inverter. This is why they inverter relies on an external clock source and shuts down if one is not present. Disconnected from the grid you have a self contained power system and the phase and frequency relationship to the grid is meaningless but the frequency does need to be close to 60hz for any devices you maybe running on that power.

I'm starting to think that the only viable option is to have each channel galvanically isolated from the other channels.

Close, but I'd recommend that the channels can be tied together - it's the grounds which need to be galvanically isolated. You see,

(if neutral gets unplugged while relay is closed, the local metering IC ground will simply float up to 230 Vrms)

is terrifying. Have you paid attention to what you're saying? "Simply float up to 230 Vrms"? In other words, your entire system can be tied to 230 volts, and without your knowing it. Any competent electrical inspector will shut you down in a heartbeat.

You should condition your signals using either battery power or (even better) a low-voltage transformer whose primary is driven by AC on the measurement side. Use a separate amplifier for voltage and current, and if you really feel like you need to save on communication links, you can switch the amplifier inputs between your two sources. This will be rather peculiar, since your two sources are AC and DC, so I'd recommend a separate conditioning circuit for your 4 variables.

Once conditioned, you have a choice - either do a power-side A/D with optical links (photocouplers) to your measurement side, or provide analog optical transmission, such as by using a V/F converter, of your 4 signals, and acquire the signals using one or more F/V converters (you can easily put a multiplexer here). The first approach uses a minimum of A/D hardware, but it requires bidirectional optical links to control the ADC. The second uses more power-side circuitry (the F/V s) but the acquisition section is unidirectional. Your choice.