If you run the hot pins from a balanced output to the centre pins of a stereo rca input, and run the neutral pin to both of the rca neutrals, can you then achieve a balanced bridged output between the positive speaker terminals, assuming each channel is single ended?
Almost there, your terminology is wrong and your method also missing a bit.
Take one XLR connector, i.e. one channel. Put the hot into the left amp channel RCA signal/centre pin. Put the cold into the right amp channel RCA signal/centre pin. Put the ground into both channels RCA screen/outer, i.e. split or chain the ground. Use the ground on the XLR pin not the connector outer.
Now you are driving the amp bridged and connect the speaker across both +/red terminals, left and right. Bear in mind each channel is now seeing half the impedance, so your amp must be rated at 4 ohms each channel with an 8 ohm bridged load.
You need another amp to connect in the same way for your other XLR channel.
Bear in mind also that the common-mode rejection will now depend on the gain matching across the frequency band of the whole amplifier, not just of the balanced input stage. Whether this is an issue (i.e. audible) is dependent on how long (and screened) your balanced cable is and what interference there is to it.
your balanced XLR terminated feed may not have the same, but out of phase, signal on both signal pins.
A normal differential amplifier reads the two signal pins and amplifies the difference between the two signal pins. The signal on one pin could be completely different from the signal on the other pin. A diff amp won't mind.
A bridged amplifier is quite different. It needs identical signals, again out of phase, on both signal inputs.
What Andrew is getting at is that some balanced outputs are not really phase and anti-phase signals, but the cold is just a form of signal return that works in conjunction with a balanced input to perform the job which is high CMRR.
The requirements for signals into an amp to bridge it are that the signals must be phase and anti-phase, as you need both amps to swing voltage. If you used the type of output above then you would get no more power than not bridging.