The Otto Cycle of internal combustion engines is as follows:
Piston goes down and sucks in air and fuel.
Piston goes up and compresses air and fuel.
Piston goes down with cumbustion pressure.
Piston goes up and spits out cumbustion gases.
Repeat.
Would it increase efficiency to introduce an elliptic or eccentric gear or cam profile that would make the piston speed variable?
A slow downstroke to increase the time available to draw in air and fuel, and also to maximize the available combustion stroke pressure?
Piston speed varies plenty anyway, due to the relationship between a vertical motion and a rotating crank.
You seem to be suggesting a longer stroke during combustion to maximise the force produced from the fuel burn, since there is a complete cycle available for induction there does not seem to be any advantage to be gained.
You are also neglecting the effect of exhaust pipe design which is designed to produce waves of negative pressure which assists in scavenging the burnt gases and improve the induction process.
There are all sorts of novel ways to change piston leverage/rate etc but most of these were tried in the '30’s and have already proven less than succesful, either the engineering was too difficult or they were just way too expensive to produce.
Modern enignes tend to have an ‘oversquare’ aspect where the bore diameter is equal or greater than the stroke, this allows higher revving engines which is one easy way to produce greater power.
Reciprocating engines have inherant losses due to the accelarative and decelerative forces within them but as yet fully rotating engines are not as economical to run and present materials and engineering challenges that have not yet been fully met.
Timing would be a real bear on that… Yack. More things to break…