Does crossover make a difference in efficiency?

I agree. The efficiency of the speaker is probably dictated
by the efficiency of the naked woofer after mating it to its LF management with the cabinet loading. The tweeter is then padded down to match the woofer. The woofer probably is running only a low-pass, and if there's an inductor, I would suspect that Totem's using a good enough one so that compression issues aren't the cause of your hearing it as
inefficient. You could add another woofer for an additional 6 dB, and hope there's enough tweeter there, after completely redesigning the crossover, cabinet, and hence, a whole 'nother speaker!
There's no free lunch here....

Dont think you can get much more out of that woofer anyway.

Strongly advise against "self-tweaking"-- the manufacturer has spent lots of time working out the right crossover for your model! W/out a crossover, efficiency would increase but uniformity of sound could be lost; units have varying impedance ratings that, in turn, may vary across the sound spectrum (this is taken into account when designing the c-over). Likewise, with external tweaks you might lose the corss-over points... a mess! Best talking this over with Totem.

Cheers!