I feel reserved about this idea, but that’s because I have assumed you’d like to play this “bass shamisen” the same way as a regular shamisen. But you said you cannot afford a shamisen, I wonder if you have learned how to play shamisen at all. With this question and assumption in mind, here’s what I think, and some guess.
Right, futozao shamisen has some low notes, so does regular guitars. First of all, though… electric guitar or bass, to my knowledge, use pickup to generate electronic signal, which is then converted to sound through speakers. Players can control the attack and release, but there’s in fact little characteristic to their tone without any effects. So in my mind, electric guitar and bass are not to be mixed up with acoustic instrument, and those using microphone attachment for application.
Electric bass use thick strings, but doesn’t need a resonator, therefore its body remain small, and one can play in similar position as guitar. Otherwise, think of double bass, the acoustic version, it has a much larger body as resonator.
So yes, the idea of bass shamisen, in theory - dou has to be bigger (to resonate with lower frequencies - longer wave length,) or sao has to be longer (longer string, lower frequency), or strings have to be thicker (more mass, lower frequency.) I am a professional piano technician, so… that gives you an idea of my understanding from working with 8 octave worth of piano strings, from small upright to 9 foot grand.
If the instrument is to be played acoustically, the question is, how much larger can a dou be, or how much longer can the sao be, in order for one to remain the same playing position? The act of plucking the string with bachi relies on resting part of one’s arm on the dou. If dou is made large, would the arm be long enough to reach? If it’s made deeper, would the arms be able to wrap around? The sao length is limited, because the left hand has its technique which require enough space for movements, like hijiki.
“oomf” seems to implies very low frequency. If the dou is not big enough for the low pitch, it wouldn’t bring you the “oomf”. If the sao length is limited, your only choice would be to get thicker strings (mass increase, frequency decrease.) When strings are thicker, you will find plucking harder. Then, maybe you will have to use a really thick and stiff bachi to withstand the increased plucking force. Depending on how low pitches you are looking for, shamisen playing does require adequate string tension to create the snap sound. Less tension, lower frequencies. Little tension, little snap. But again, if bachi were heavier, it wouldn’t snap as easy. If plucking thick string would work, it’s going to sound different anyway because a low pitched string brings out way more audible overtones than a higher pitched string. Again, we are talking about acoustic instruments.
Using piezo microphone seems most straight forward method of amplification, using pickup requires metallic wire. I guess no one says you can’t use metal wires, but different material will give different sound. Metal wires might damage bachi much quicker.
Since you mentioned “iconic sound of shamisen”… in my opinion, the “iconic sound” has been created within a certain pitch range, and by instruments of certain specifics. What you have been describing, a bass shamisen, is another instrument after all.