Is there a way to balance the radiators so even the far ones get steam without suffocating everyone in the rooms closer?
Air valve sizes.
They generally reccommned larger sized valves further away from the boiler to draw up more heat.
You can play with the valve sizes.
Change the ones closer to the boiler (downstairs) to a smaller size and see if that keeps the heat downstairs reasonable, while the upstairs gets enough heat.
Change the cold rooms to valves with much larger openings, and see if that helps.
Do both - smaller closer to the boiler, larger in cold rooms.
To change them: When the heat is down!! unscrew the valve. put teflon tape on the thread of the new valve. screw in place. wait for the heat to come up. check for leaks, and screw in tighter if there are any.