[2009Toyotoad]

Too much advance creates a detonation issue, which on most modern powertrains means the ECU/ECM will automatically force timing retard to protect the engine.

The others options to play with are throttle control and cam lift/ profile. Cam Lift which modifies both the size of the valve openings and the duration. Note this part becomes tricky and varies from one engine design to another. Basically, some engines by their design won't support cam modification and will perform poorly in both power and fuel economy on any profile other than OEM Spec. The ford cologne 2.9 V-6 is a well known example of this.

Throttle control come in two flavors mechanical and electronic. Electronic works with drive by wire and requires the purchase of throttle controller unit and a bypass or boomslang wiring harness to intercept signal from sensors and recalibrate responses to those signal as outputs the the throttle control itself and the relative throttle range. Basically, if someone mashes the gas pedal they will only get a percentage of full throttle and rather than instantaneous response to the sharp stab at the pedal, the throttle only opens at the speed the throttle controller is programed to allow.
Mechanical throttle controllers are for cars without drive by wire technology and requires the use of governors, stop steps screws or bolts, and heavier throttle springs. The most common usage of this type of control was in commercial trucks and 4X4 vehicle where excessive throttle input... "stabing the pedal"... created safety or economy concerns.

VVT or variable valve timing takes advantage of valve open/close duration timing. The valve does not open any farther but it stays open or closed longer in the piston cycle.

These engines compensate for possible timing retard by the ECU/ECM by allowing the position of the VVT sensor to control timing advance or retard.

"To a certain degree" add on electronic throttle controller devices can be used to "tweak" the timing advance to optimal fuel economy over / power and performance. However, it is a rather narrow range of adjustment in which to play. Too much advance and the Knock sensor signal to the ECU to retard timing regardless of the input from the VVT sensor.

The electronic add on throttle controller can't force the ECU to ignore the sensor signal all together. If it could the ECU would start issuing DTC codes and light up the MIL on the instrument panel. i.e. "Not Good"

Trying to achieve the same kinds of control via mechanical throttle controller is a whole book or series of articles and debates within itself. Let's just say there are a myriad of ways to achieve that type of control and each has its benefits and pitfalls. Nobody ever gets it perfect and it always needs tinkering and modifications. As always successful mechanical throttle controlling varies by weather, driver, driving conditions and the vehicle itself.

Atkinson versus Otto cycle engines: the key here is where in the piston position cycle is the fuel/air charge ignited by spark. There are actually very few true Atkinson Cycle engines in cars. hybrids like the prius are actually "Atkinson like" cycle engines rather than true Atkinson engines. Otto engines ignite the fuel charge just before top dead center on the piston stroke, Atkinson at top dead center or slightly after TDC. For more of modern transportation the Otto theory was preferred other the Atkinson. Ignition at TDC added a stress load to the crank shaft and wrist pins, rings, piston, and bearings. Modern engines using the "Atkinson like" offset the position of the crankshaft from the piston to lessen these stresses and increase engine durability and lifespan. There is/was a larger risk or concern of pre-inginition or "dieseling" in an Atkinson cycle but this is still hotly debated. As the control over a pre-ignition condition have advanced so much since the original Atkinson designs.

I hope that a little more clarity to your question about using timing advance. If you really want to get even more into understanding of how timing advance works look into the Wankel engine design. Once you get a sense of how timing works on that rotary design it makes for a easier to understand piston engines designs.