Heres my idea, but several other things will be needed first. The system voltage will need to be much higher, somewhere between 36V and 60V. The only thing operated by a belt will be the generator, and it could be direct drive. The oil pump mechanical, but everything else driven electrically.
Now a V6 would have the exhaust system between the heads and the intake on the outside, just the reverse of how it is done now. The engine will need two exhaust valves. All the valves will be actuated by a solenoid that is controlled by the PCM.
The exhaust valves from each cylinder will fed into separate manifolds, one manifold will be direct exhaust, the other will be a plenum that connects all the other valves together but will have a separate gate valve to dump exhaust to the direct exhaust system.
The engine will operate in two modes, one as a 4 cycle that we know today with the gate valve in the plenum open to the exhaust system.
For light loads, the plenum exhaust gate valve will close and the engine will go into a 6 cycle mode: intake, compression, power, primary exhaust, expansion and then second exhaust. During the primary exhaust, only the exhaust valve to the plenum will open and the same valve on the cylinder in the expansion stroke will also open.
The exhaust from the first exhaust stroke will duct into the cylinder on expansion stroke and push that piston down, effectively nullifying the pumping losses. When the expansion stroke is finished, that cylinder will close the exhaust valve to the plenum and open the other exhaust valve to the cats and tailpipe.
The solenoid valves will also allow an infinite number of valve timing profiles to perfectly match to the load requirements for each revolution of the engine. Fewer gears would be needed in the transmission because the most efficient operating RPM would be so wide.
The engine would also have a high compression ratio but the intake valve timing could be adjusted so that the effective compression would be variable. Keeping the intake open part way in to the compression stroke would lower the effective compression ratio. This is called the Miller Cycle, short compression stroke, long exhaust stroke, but under the right circumstances, it could go full compression and operate as a gas diesel.
On the highway, a small displacement v6 with a turbo charger in 6 cycle, gas diesel mode, I could see some very high gas mileage numbers possible. Maybe even the elusive 100 mpg in a compact car like a Civic.