The solution we have come up with is a "Five Bar Crank Mechanism", this mechanism takes the place of a conventional Crank in the slider crank mechanism, the following animated imagery is self-explanatory about its kinematics, and the comparison shows how much rotary force is acting on the Five Bar Crank Mechanism than on the Conventional Crank in the Slider Crank Mechanism.

 The Five Bar Crank Mechanism has two distinct characteristics from the Slider Crank Mechanism,  

1. The Five Bar Crank Mechanism does not have a constant crank radius, which means the force action point varies around the crank center and

2. The angular displacement of the crank is not symmetrical between the forward and the return stroke.

These features help in more efficient linear to rotary force conversion over the slider crank mechanism.

 Also

1. The Five Bar Crank Mechanism has a positive rotary force acting on the crank at the TDC position than on the Slider Crank Mechanism.

2. Since the Five Bar Crank Mechanism has a positive rotary force acting on the crank at the TDC position, this mechanism transforms most of the cylinder pressure into useful rotary work before the pressure drops in the cylinder.

Which meets both the requirements of the problem statement.

Analyzing the Five Bar Crank Mechanism in MSC ADAMS software, for its ability to convert the linear force in the cylinder to rotary force useful work, we arrive at the results below:

 The simulation results are based on kinematic data as mentioned:   Crank Lengths - 100mm, Intermediate Link - 70mm, C-Rod Length - 300mm, and a Constant Load on piston - 100N.

The simulation results of Piston Displacement and Crank Torque plots are charted against Crank Angle.

 The Piston Displacement and Crank Torque plots of the Five Bar Crank Mechanism (---5BCM profile in red) and Slider Crank Mechanism (---SCM profile in black) are compared in the above-animated image.

The Crank Torque plot shows that the Five Bar Crank Mechanism delivers more torque against the Slider Crank Mechanism, this plot also indicates that the five-bar crank mechanism has a positive torque at the TDC position of the crank as opposed to the slider crank mechanism.

 Result:

The engine efficiency is significantly improved by increasing the area under the Crank Torque plot when compared to the slider crank mechanism.