Hi Probiote, and welcome to Theremin World.
Yes, get the bass mod. It won't give you twelve octaves, but it will go down to about 5 Hz and if you ship your etherwave to Thierry for fitting he can tune it to extend the upper end as high as it will go, which will be enough.
To get that gorgeous gnarly sound in the first video you want a ring modulator. My choice would be a Snarling Dogs Mold Spore - if you can find one second hand. It's a combo ring-mod and wah and will let you adjust the carrier signal for the ring-mod with your foot while you play for extra freakiness. (Note the mold spore has a noise gate, so requires the effects loop mod I mention below.)
Alternatively, as Christopher suggests, an octaver will take the range of your theremin down, and also gnarl up the sound by taking it closer to a square wave.
For the sound on the second one tossing a simple distortion (or fuzz) pedal into the chain will do the trick, but you might experience a lot of hiss when the theremin is muted with the volume loop. Or if you're really unlucky you'll have a distortion pedal with a noise gate - great for guitars and horrid for theremins. Either can be circumvented with an effects loop mod for your theremin so that you can apply the distortion before the volume is attenuated by the expression circuit of your instrument. Again, ask Thierry.
It it is tricky to get a sufficiently short attack to make a well punctuated bass line - it can be done by hand (see Pamelia's Kurstin's TED talk on YouTube for an example) but if you're planning on keeping it going throughout a long piece with a tight beat, consider a Gig-FX Chopper which will modulate the amplitude of your playing with either a square wave for a plucked sound or a sine wave for that dub step "wub-wub-wub" sound. Or a combination of the two. As it is, like the Mold Spore, a treadle, it will give you the option of varying the effect with your foot whilst playing. If you get the more expensive version, the pro-chop, you will be able to sync it over MIDI to keep it really tight with the rest of the band.
if you're modulating with a square wave I'd toss in a reverb to emulate the "release" portion of an ADSR envelope shaper. A slap-back delay will turn every "dub" into a "dub dub", which might be cool, and some slow flanger or phaser would add variety to the sound.