How can I switch two wires using solid state relays?
The circuit is simple enough:- just wire the inputs of each pair of SSRs in series, and power them through opposite sides of a toggle switch. A single resistor will set the LED current of either pair. The toggle switch provides automatic 'break-before-make' action.



However this may be a bad idea for several reasons:-


You need AC relays. AC SSRs generally use SCRs or TRAICs, which have output attributes that make them unsuitable for your application - including high voltage drop, turning off at every current reversal, requiring several volts to turn on, and slow switching speed (not good at high rpm or when using PWM speed control). 
PhotoMOS SSRs have lower voltage drop, and stay on continuously (so switching speed isn't a factor), but are primarily DC devices. To handle AC requires wiring two FETs back-to-back in series, which doubles voltage drop and power loss. 
High current PhotoMOS relays are expensive!
Even the best PhotoMOS relay will drop some voltage, causing an imbalance between the two switched phases and the third un-switched phase. A sensorless controller relies on symmetrical back-emf waveforms to get accurate commutation timing. Distorted back-emf may cause rough running, lower efficiency and loss of sync at high loading (this isn't a problem for a sensored motor and ESC, but then you need to also swap the sensor inputs to the ESC).
You must ensure that the motor direction cannot be switched while it is running. Unlike a reversing controller which knows how to change direction, your ESC will not automatically slow down to a stop and restart when you switch the wires!         


An H-Bridge won't do the job either. The best (and obvious) solution is to use a bidirectional brushless ESC.