Forget about the negative PWM excitation signal and bias the positive PWM signal up so that the AD620 is always dealing (on both inputs) with a voltage within its input common-mode range.
Note that the AD620 will need a supply of at least 4.6 volts so 3.3 V is completely out. So, if you went for a (say) 5 V supply, the input common mode range is between +1.9 volts and +3.8 volts. Read the DS for details.
Once everything is set up to work with the correct voltages, the AD620 output is: -
(gain)*(A-B) + ref_pin_offset
where A and B are the voltages at the inputs - note you don't need unipolar supplies or excitation to make this work but you do need adequate supply rails and attention to the common mode input voltage range.
You should also note that if Rx imbalances the bridge too much you will get a progressively bigger error term in your reading because, despite what you may have learnt, a quarter bridge (that's what they call them when only one resistor is active) has linearity errors: -
Of course you could go for a constant current feed (still OK with PWM) you would halve that linearity error: -
It's also worth pointing out that slew rate limitations on dealing with fast edges (due to PWM) may well induce other errors from the AD620 so, have you considered the impact of this - maybe try simulating it and adding filters before the inputs to the AD620.
Remember that the AD620 is still pretty good with DC excitation having an input offset error of typically 30 uV.