Best way to reduce duplex boiler heating expense?

[Elliot Cole]

I own a duplex where I pay heat for the property. As an added quirk, the downstairs unit contains the thermostat for both units. The boiler is the only thing in the property using gas and last year my bill was over $2600. I've priced out upgrading to a high efficiency model and the quotes vary from $5,000-$11,000. An alternative proposed by a recent HVAC company was $1100 to flush the system, bleed the radiators, and leave the existing boiler in place, but install an ecobee wifi thermostat where I can set the max allowable temperature remotely. Which options make the most sense and what sort of pricing is reasonable?