Shoutbox

While your reasoning about why it should be possible is sound, the practical difficulty is that there isn't any writable "hard disk" that you can gain access to and put a few files on.  You can only flash the entire firmware in one go, so you would have to first obtain some, then figure out how to modify and flash it without bricking the device. This might require finding and exploiting some security hole in the currently loaded firmware, because firmware images are often cryptographically signed and you shouldn't expect to be able to load your customized one through the normal process.  That's a lot of highly complicated work, which probably requires skills neither of us has.

As shawnz noted, you'd stand a much better chance with a router supported by OpenWRT.  With those, others have done all the homework, there is an existing customizable firmware code base and documented procedures for building your own.  I am not aware of any such project existing for Speedstream and I think we can safely say you are probably not going to be successful at doing this on your own -- of even if you are, it definitely won't be worth the time it will take.