Third floor steam heat radiators almost never get any heat with new ecobee thermostat

I found a HeatingHelp thread addressing similar issues, but from years ago, so I'm starting a new thread.
I live in Chicago, in the city, in what is commonly called a “three flat.” It essentially looks like what people in other parts of the country call a brownstone. Mine was built in 1906, so it’s very poorly insulated, and it has single-pipe steam heat provided by a Weil-McLain boiler. My house basically was three identical apartments stacked on top of each other. In the late 1980s or early 1990s, the building was converted into a single-family house, though, in many respects, it retains the original floor configuration (but there is not, for example, a kitchen on the second and floors, as there had been). My house, then, is a very vertical (and free-standing) single-family house.
The radiators are the original radiators, though a few were relocated when the house became a single-family home. The house is expensive to heat, but, despite the (essentially) insulation-less walls, the steam heat provides reasonably good, reasonably comfortable heat.
However, approximately a year ago, a HVAC contractor replaced the SpacePak air conditioning system that we installed when we purchased the house a long time ago. When he did so, he replaced the existing, older Honeywell programmable thermostat (digital, but not wireless) with an ecobee thermostat, which I love, but for the following:
The radiator is where it has always been since I’ve lived in the house, on the second floor.
I don’t understand HVAC systems very well, so I’m sure I will not use the correct words, but the third floor radiators (where we have our master bedroom, master bathroom, etc.) barely gets heat anymore, and, as a consequence, the third floor is very cold at this time of year—uncomfortably for me, and almost unbearably so for my girlfriend.
The only time most of the third floor radiators get warm at all, and so the only time the third floor is even reasonably comfortable, is when we wake up in the morning. This, I am sure, is because that is when the boiler is on for considerably longer as it must raises the house from the nighttime temperature (63) to the daytime temperature (67, a temperature it now holds every day during the pandemic, while we work from home and are essentially home-bound).
I want to emphasize that the ecobee is not having a problem maintaining the nighttime or daytime temperatures. It does this well. But, however it does what it does, it does what it does in a way that’s meaningfully different from how the Honeywell did what it did, at least in the sense that the ecobee has turned the third floor into the Siberia of living space. We didn’t have this problem with the Honeywell.
The only good news there is that we spend less time on the third floor than on any other floor, and we’re mainly on the third floor in the early morning and evening.
Is there any way, without causing me to incur even more substantial heating costs, to rejigger the ecobee so that it also drives some heat to the third floor? For me, this is not only a comfort issue, but also is of concern because of the threat of freezing/burst pipes in the third floor bathroom area, where there no radiator in at least 20 feet that EVER gets even warm to the touch. Sure, some home heat finds its way to that area, but ill that be enough to protect against that threat? I don’t know ….
Thanks!!