This system just keeps cycling

I have a natural gas gas furnace installed into my home.  It relies on a duct system to carry heated and cooled air between the gas furnace and the rooms of the house.  The conditioned air passes through the ducts, picking up dust, bacteria and other contaminants, and then is introduced via vents cut into the ceilings.  These pollutants are circulated throughout the condo and breathed in by my family. Because the heat is introduced from overhead vents, the warmest temperature is consistently up near the ceiling, where it does no fantastic at all.  Down by the floor, the air is often rather chilly, forcing me to raise the thermostat setting. The gas furnace then blasts a tremendous amount of warm air, continuing to work until the thermostat setting is achieved. It then shuts completely off, creating very unpleasant temperature variations.  This process is loud, aggravating and costly, then the gas furnace requires frequent maintenance. I need to update the air filter every month and hire a professional Heating, Ventilation, and A/C specialist to maintenance the device every fall. I also need to worry about the condition and upkeep of the duct system.  If there is a problem with the gas furnace, I am constantly worried about potential carbon monoxide poisoning. I wish I could afford to tear the duct system and gas furnace completely out and update them with a hydronic heating system. I’d appreciate to install a boiler in the basement and radiant heating under the floors in every room.  Radiant heated flooring is completely noiseless, requires little maintenance, and the heat originates at floor level. It rises very slowly and evenly, with the warmest uneven temperatures remaining closer to the ground and allowing lower thermostat settings. There are no drafts or frosty spots, and radiant heating doesn’t introduce contaminants into the breathing air.