I used to run a speaker building club when I was a teacher, so I think this is potentially an interesting project.
But I'm not clear what is meant by 'sustainable methods to create a low cost, high fidelity speaker'. It seems to me that the three goals are in conflict with each other, which, ironically, may be a plus, since you have been given a serious challenge to try to answer - a simple problem would be easier, but you wouldn't learn much.
The most sustainable speaker is none at all - make music yourself, listen to others, and so on. But for many, this isn't an option.
So then the question is what is sustainable, but that crashes into the low cost and high fidelity requirements - it is simple to make lousy cheap speakers, and not so hard to make fabulously expensive speakers that are (one hopes) better than cheap speakers. And often the solution to the quality/cost demand is very expensive in terms of electronics - if you can use an enormously powerful amplifier, you can get away with smaller and less expensive speaker components - drivers and cabinets.
I would suggest looking at alternative cabinet materials - multilayer corrugated cardboard or expanded foam. Obviously the corrugated cardboard might be more sustainable, but multiple layers make for a bigger cabinet, which makes for more expensive shipping. I built some speakers from six or seven layers of packing boxes, and they were remarkably unboxy sounding, but they were huge. Advent made some very nice sounding speakers (and affordable, too)with expanded foam (Advent II?0) but they didn't look like what people wanted speakers to look like, so the particle board boxes outsold them even if more expensive (if memory serves).
The other factor to think of is full range drivers - fewer drivers mean less manufactured junk, and an easier speaker to drive with the amplifier. No inexpensive speaker can be actually full range, but even modestly priced drivers can sound balanced and full(ish). And since relatively few people actually have real full range systems, it is clear that good enough is fine with most people. So focus on inexpensive drivers that have some bass and treble extension.
Good luck.
