I'm surprised you haven't gotten the Safety Police on your case yet, so allow me to step in
Code typically requires some sort of a fire-resistive barrier between an attached garage and the adjoining living space. Typically this means something like 5/8" type X drywall (taped and mudded with at least 1 coat) a 20 min rated fire door assembly and to have any penetrations sealed. A duct between these two spaces would send most inspectors into orbit for that reason. Risk of fire spread, CO, flammable fumes, etc make the duct idea very bad.
By far - the cheapest and most efficient route is a dedicated nat gas heater in the garage controlled by a T-stat in the garage. You can get sealed combustion, which is wise, and if it ducts in outside air for combustion and exhausts outdoors too, then you are in the best of all worlds. The ceiling mounted units with a fan are perfect for garages. My neighbor has one and it is awesome.
Electric is workable, but it takes a lot of power to get decent heat and is expensive to run (but cheap to install). Any time you take a step from an energy source to some other form, you lose a lot in the transition. You burn some fuel to make heat to make electricity, and then turn the electricity back into heat in your house, losing energy at every step. Going straight from fuel to heat is by far the most efficient route (within reason). Electric is nice if you cannot get easy access for a gas line, for very rare usage needs, or if you want a temporary solution. I have 2 electric heaters in my garage - 5000W (30A 220v circuit) and 4000W (20A 220v), and they cannot make my (insulated) garage decently warm unless it is mild out - but they can sure make the meter spin! I do not have good gas access in there and they are temporary in my case, so I deal with it.
I wouldn't worry about any extra maintenance coming with a new heater in the garage. There isn't much to them, and they are only intermittently used. Watch Craigslist for used garage/warehouse/dock heaters. Many will be too big, but good sized ones come along. Or just bite the bullet and buy new. You will spend a ton on making your house duct ideas work, so I don't think it would save you anything that way, and the safety compromise is not worth it, IMHO.
Get a gas heater, run a gas line, run a vent/intake, plug it in and go.