Benchmark AHB2 - To 'mono' or not to 'mono'

What George said, bridging doesn't improve the sound quality, it just gives you more power for higher SPL, but it reduces the amp ability to drive low impedances.

Do you see the clipping leds on the AHB2 constantly flashing? If not, there's no need for more power.

For the damping of the membrane movement - speaker's own impedance is in the series with the amp's output. Most of this impedance is resistive.

A speaker relies both on mechanical damping and electrical damping, its Qms and Qes parameters; Raidho for example expressly recommended high damping factor amplifiers for their speakers as their woofers had high Qms and relied on the electrical damping of the amplifier. There are threads on trying to find a suitable amplifier for them as their bass would sound loose and bloated with low and normal damping factor amplifiers. Just compare a Pass and an Audionet amp and you will see how their bass is very different; the Audionet's bass is much more damped and dry with better transient response, but it can sound dynamically constricted with low Q overdamped speakers

Since the OP's Pulsar Seas woofers have more mechanical damping they may not need too much electrical damping from the amplifier; bridging the amp may offer a more dynamic bass if the stereo amp/speaker pair is overdamped.   

Actually you might perceive an increase in dynamics with 2 amps bridged, not due to more power but due to the decreased damping factor of the amp.

A lower damping factor will make the amp sound less tight and it may give you a slight bass bump at the speaker resonance frequency.

Since the Pulsars are an easy load there's no harm in trying.