Measuring AC and DC earth ground referenced signals
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.