How to track energy usage per zone?
Since tenants are involved, you'll need to do this right

If you were owner-occupying a zoned single-family dwelling, then taking shortcuts in the interest of expediency would be an acceptable way to get rough estimates of zone energy usage for your own uses.  However, you're not in that situation; you're dealing with tenants instead, which brings real estate leasing (landlord-tenant) law into the picture.  While state and local policies and attitudes towards submetering vary, your best bet to get AHJ (and tenant!) acceptance is to do this the right way from the start.

Fortunately, you aren't the first landlord to have this general idea, so prepackaged BTU metering systems are available, generally running about $700-$800 a zone for an Istec 4440 or a Badger 380.  These consist of a flowmeter with totalizer/register and two pre-harnessed temperature sensors for supply and return.  The meter is installed in one of the two pipes going to the unit (the Istec goes in the return line, while the Badger doesn't care), while the other temperature sensor is fitted in a thermowell in the other pipe.

From there, the two diverge.  The Badger 380 requires 12 or 24VAC or DC power (a standard 24VAC, 40VA HVAC control transformer should be ample, even for several meters, though), and has to be programmed using a Mini-USB cable and the supplied commissioning software, but once that's done, it not only can output simple pulses to an external totalizer, but can speak BACnet or Modbus over RS-485 to some sort of central monitoring system (anything from a Pi with an RS-485 hat, to a full-on BMS such as one'd find in a large building).  The Istec 4440 lacks the network connectivity support of the Badger 380, but has a built-in LCD register (something the Badger 380 lacks), and is battery-powered; it does support pulse outputs to an external totalizer, though.

Either way, you can get within a few % of accuracy here, which is about as good as you'll get without spending much, much more on high-accuracy flowmetering hardware, as ordinary water meters aren't rated for hot-water hydronic duty, and are only held to 1.5% accuracy by AWWA standards, anyway, just for flow.  Given that we're dealing with a derived parameter (BTUs) here, 2-3% accuracy is not unreasonable.

Other legal issues

While Maine landlord-tenant statutes, as far as I can tell, do not directly touch on submetering, they do have the fairly logical prohibition on a tenant paying for common area heating service without expressly and separately agreeing to do so.  To avoid running afoul of this, I would put a BTU meter on the commons area zone or zones as well; this way, you can apportion fuel costs fairly among all participants, with you, as the landlord, paying for commons area heating and each tenant paying for their own unit's space heat.

Also, you may need to provide heating cost information for the past year to your tenants on request with the note that space heating costs will be apportioned based on BTU usage, and presumably will note the presence of BTU metering on your Energy Efficiency Disclosure Form.  See 14 MRSC 6024 and 14 MSC 6030-C for details.  You'll want to talk to a lawyer about amending any written leases, too, and any written billing you may do.  I would at the very least make heating costs into a separate line item on the billing, or otherwise make it clear that they are not fixed, unlike the rest of the rent.