" Is there anything we can do to get the cost fairly split between the two units? (We also pay for the washer and dryer usage between the two units.) "

Well you could try slapping the landlord around until she hired someone to hook ecah side up to their respective meters. You could beg and plead with landlord but I'm sure you already tried that. You could go to your breaker panel and flip the breaker to other side's "heat tape". The tenant will complain to landlord that they have no heat and landlord will hire a contractor to fix their "heat tape". Contractor will hook the heat tape to proper panel and everyone will pay their fair share going forward.