(Shrug) There is no good solution, because it's the wrong problem. We shouldn't be using AC at the home/light-industrial level at all. No matter how efficient the inverter is, it's going to be constrained by the inefficiency of putting switching regulators in everything from wall warts to machine tools.
That's the part of the situation that needs to change, but of course it's the chicken-and-egg problem from hell...
DC in the house doesn't remove the need for switching regulators - you still need to step down from the house voltage to the device voltage. Don't forget that devices that accept 5V or 12V from a wall wart almost all still have switching regulators to step down to 3.3, 1.8 or less. It does remove the need for transformers and rectifiers, which would buy us some efficiency.
And don't forget that if the house DC supply was at less than 120V, then you'll loose more power in the house wires, because the electrician who wired your house was too cheap to buy superconducting romex.
If your house is wired with the lights and the outlets on separate circuits (mine is, because I'm an EE and I built the house), you could change out all those lights to low-voltage LEDs and supply 12-24VDC to them and light up your house just fine on the 14-gauge copper romex that's in your walls now. This works because the required current would still be well below the 15A at which the wire is rated. (Getting your electrical inspector to approve it might be another matter, though.)
In some cases, this trick would work for the outlet circuits too because most of the things we plug into outlets now are low-voltage DC wall warts, and they could be replaced with low-voltage DC-DC converters. The problem is that your refrigerator and your dryer are not run by wall warts, so outlets are tougher to convert to DC than lights.
True, I should've written "rectifiers and filters." The inductor(s) are most likely still going to be needed, but you can get rid of the diode and filter capacitor losses on the primary side.
That's likely true, since DC motors need either permanent magnets or energy-wasting field coils. But motors are only a part of the energy-usage picture.
Ideally, we'd distribute "last mile" power as DC, and devices that really need AC would handle the conversion themselves. For instance, a polyphase inverter that's designed to drive a specific motor would be more efficient than a general-purpose single-phase inverter of the sort being discussed here. So even motor-drive applications could still be a net win for DC distribution.
AC gives you cheap synchronous magnet motors. These are what you find in most off the shelf power tools. But, they can;t be electrically speed varied, and don't produce max torque from a standstill (treadmills for example use DC motors for this reason).
Its not a show stopping constraint anymore - so much so that a ton of electrical appliances can happily run directly off of 200-300V DC because it just bypasses their internal rectifiers.
That's the part of the situation that needs to change, but of course it's the chicken-and-egg problem from hell...