Would increasing the cabinet volume improve the speaker at all? Or would I have to go back to square one regarding the crossover?
The crossover frequency is far enough away that you would not have to change it.
This is a standard sealed box system and therefore the woofer (if the front baffle were mounted flush to a wall) has a 2nd order high-pass transfer function in the bass. The response is completely defined, for small signal drive where distortion is low, by Fc, Qtc, and driver efficiency.
Fc is determined by cone mass and the combination of the suspension stiffness and the air spring. A bigger box lowers Fc by providing a more compliant air spring and Qtc goes down because of the change in reactance at resonance.
The lower Fc provides more bass extension but the lower Qtc reduces the output, slightly, around Fc. The problem with a very small system such as this, is that the woofer does not have much Xmax, and more importantly volume displacement, which means that the woofer will easily overload with heavy bass lines at high output. A higher Fc reduces Xmax below Fc since the rolloff is faster and less Xmax is required at higher frequencies for a given SPL. The higher Fc with higher Qtc will have more output and more displacement at Fc but it is the lower frequencies that will tend to overload the driver faster.
Fc in the unmodified system is somewhere over 100 Hz and if the source material had no content below Fc then in this particular case the higher Fc system would have more displacement. But most music has lots of content below 100 Hz and the increased extension with a bigger box and lower Fc would then lead to increased displacement.
Bass boost also increases displacement and if you find that you can get enough level with some bass boost then you might want to try a bigger box. Keep in mind that as you increase the box size Fc will asymptotically move closer to the driver free air resonance (Fs) and it takes an infinitely large box to reach Fs. There is a point of diminishing return in increasing the box size.