How to HVAC service 3 floors without ducts in roof?
HVAC is most efficient when you blow in the cold air from above and let it settle down. This gives a very even temperature gradient from head to toe. Just blowing it in from the floor will make your feet cold and your head hot, causing you to lower the thermostat and drive up your operating costs.

It is worth the effort to install the ducting in the ceiling or at the ceiling level, wherever possible. It may seem inelegant, but it's a good idea.