Plate chokes won't have anything to do with inversion per se, but if they are of the proper values you get comparatively low DC resistance and fairly high AC impedance, so it can give more voltage swing for a given plate voltage since its not losing a bunch in a resistor. The negative supply does work with a CCS to give more potential voltage swing too. It can be done with a resistor as well if you wanted to, allows for a much bigger tail resistor without giving up a ton of voltage across the tube. That inverter should have serious voltage output potential for comparatively low supply voltage.
I thought the whole appeal with the CCS is that you didn't have to pay any mind to matching, it just made it work regardless of tube particulars. Somewhere I've seen tests done using a CCS to force completely different triodes to give balanced output.