[Frostynorth]

Ductless splits are nice, super quiet. Sounds as you want a full forced air system though.

An existing building ductless requires a lot less work, they are reliable, but replacement parts are expensive.

A setup with four of five heads could cool down those rooms, and be less expensive to run when rooms are unoccupied.

I've installed both (except running ductwork) and each has their benefits.

Many ductless are heatpump setups so they can cool and heat.

If I were building a house would just go forced air. They're overall simpler to service, easy maintenance (change filter, clean condenser, and get the gas heat checked once in a while - though I never check mine). Parts are much cheaper to replace as there are no complicated boards or electronics.

If it was just a room or two, or running duct is complicating the design of the house, ductless splits are pretty cool. If they're properly installed, there should be no major issues.

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Where I live, natural gas/LP heating is pretty much required, as it's much cheaper to operate than electric. Gas furnaces are getting 96% efficiency. Ductless heatpumps can't generate enough heat when it's -30, they're good to about -10c. Still wouldn't bother.

I've spent hours trying to resolve ductless problems when they arise, it's ended up being boards (there are multiple) or compressors. The electronic expansion valves have been reliable.