[Andyman]

If you advance the camshaft you might be advancing the ignition timing at the same time because the distributor is usually connected to the camshaft. Advancing the ignition timing can make the engine more efficient and may have a greater effect than the change in valve timing. If the engine has a crankshaft position sensor then the ignition timing probably depends on the crankshaft instead of the camshaft. In this case it might not be a good idea to retard the camshaft because the lower cylinder pressure requires a more advanced spark for optimum efficiency and there is no adjustment to change it. Possibly you could increase intake air temperature instead to speed up combustion.

If the camshaft is set more retarded then the engine can tolerate a little more advanced ignition timing without knocking. This combination is likely to give the best fuel economy. If you retard the camshaft and it retards the ignition timing at the same time, I would expect lower fuel economy.

I have another Honda with a SOHC engine, a '94 Civic with a 1.5 liter 8 valve engine and 5 speed transmission. It has an old worn timing belt. I tightened the belt tensioner pulley so it wasn't as loose. That has a side effect of retarding the camshaft a little. Then I advanced the ignition timing a little. I took a long trip and the car averaged 50 MPG when I used about 10 gallons to go a little over 500 miles. I don't know what it would do with a new timing belt which would probably advance the valve timing a little.

I think that there are two reasons that retarded valve timing should help efficiency, at least at low RPM. One is that a later closing intake valve reduces vacuum during the intake stroke, reducing pumping power loss. The other is that a later opening exhaust valve increases the expansion ratio during the power stroke, recovering more energy from the burned gases before they are released to the exhaust system.

An ideal engine would have a completely vaporized fuel mixture, have no vacuum during the intake stroke (open throttle), compress the mixture as much as possible without preignition or detonation (about 8:1), burn all the fuel before the piston moves down, keep the heat in the gas instead of heating the engine, expand the hot gas until it reaches atmospheric pressure (which would probably require an expansion ratio of at least 16:1), and then release the exhaust at atmospheric pressure during the exhaust stroke (no exhaust restriction). The Atkinson cycle gets closer to this than a normal Otto Cycle. A retarded camshaft makes an engine more like an Atkinson cycle engine. Ideally the engine should have longer duration on the intake valve so the middle of the valve overlap period can be near TDC (piston at top dead center).