Lithium thionyl chloride / SOCl2 batteries have excellent energy density but are not aimed at high-current applications and are not rechargeable, so it seems likely that you can save weight and cost by using some other kind of batteries.
Quadcopter batteries (typically lithium ion polymer technology, rated for 5C to 15C discharge rates and rechargeable hundreds of times) might be a better choice. You could use half-a-dozen 2200 mAh packs, or a couple of 5500 mAh packs.
Previous question Quadcopter liPo battery weight/capacity trade off includes some charts comparing energy densities, etc., for several battery technologies.
Note, if your application is controlling several motors, with several motor controllers, you may be able to use higher voltages to the controllers, which use PWM to deliver desired amounts of energy to the motors. This technique is usable when you have a high-voltage, low-current power source. However (see below) that doesn't help in the present case. Likewise, a DC/DC buck converter (that converts high voltages to lower voltages, at ~ 95% efficiency) doesn't help.
The 20A, 10Ah parameters of your SOCl2 example imply 30 minutes of operation. The 20A, 14.4V parameters imply energy rate is 288 W. The current drain per cell in the example is 1A (which exceeds the rating of a typical AA SOCl2 cell). If we limit per-cell current to 1A, we get 3.6 W per cell. Then the number of cells required is 288/3.6 = 80 cells, regardless of the cells' series or parallel configuration, which is why a higher voltage to the motor controller, or to a buck converter, doesn't help.