The meters shouldn't interfere with each other. They're just ammeters, after all; current is current. You will be charged for the parasitic load your new meter introduces, of course, which may vex your test.

Bigger problem is that you'll need the electric company's cooperation to turn off your circuit so you can rewire—and they are almost certainly not going to be happy about having anything upstream of the main cut-off.

You're more likely to get approval if you install a new box with its own main breaker, and make the old box a subpanel of the new one, with the meter between them. That puts the weirdness firmly inside the domain that you are entirely responsible for, and leaves a clear way to isolate it from their lines if necessary. Essentially, that's the normal setup for apartments which are paying for electricity separately; you're just setting up a single apartment.

I suspect you're going to find that the electronic meters really are as accurate as the mechanical ones, or if anything are more accurate.

Wouldn't it be easier to just ask the manufacturers of these meters what their error tolerances are? Or to ask apartment building owners who have a mix of meter technologies whether their numbers add up reasonably?

(Especially since the cost of installing the second meter is going to swamp anything you think you might challenge on the bill, never mind the legal costs of trying to convince folks that your meter is the more trustworthy of the two. If you're concerned about your bill, putting the same money into energy efficiency upgrades would be a far better investment.)

TL;DR: CALL YOUR ELECTRIC UTILITY ON THEIR EMERGENCY NUMBER

It sounds like you live in a duplex with dual services -- in that case, call your utility ASAP. What the electrician did was a very dirty hack that will not pass Code muster, and likely screw with the electrical metering -- it will also break in interesting ways if later on the utility puts the two units on different transformer secondaries.

BTW -- an open neutral is an emergency situation, as it can easily be a fire and/or shock hazard.