CMOS switch with "negative" current
Do CMOS switches work on "reverse" current as well, with just a +12V single supply?

Actually there is no "reverse" current. The relay connects an output to either GND or +12V. That makes the current flow in one or the other direction.

The same will be true if you use such a switching IC to do the same. So the switches need to be "bidirectional" which they are! So I think these ICs are suitable for what you want.

Do note that when using the ADG5434 each switch has a series resistance of up to 13 ohms so at 28 mA a voltage of up to 0.36 V will be dropper per switch so at the output you will not get +/- 12 V but +/- 11.3 V. The voltage drop will be lower for the ADG1434.