Is there any indication in Chazal (or at least in other ancient literature) that tekhelet and argaman could be derived from the same creature (as currently proposed by the Tekhelet Institute)?
According to הרב מאיר הלוי הלמן - לבוש הארון (modern English sefer on Techeiles), on page 21:
The color of murex dye was commonly known as “Tyrian Purple”, as the city of Tyre (today in Lebanon) was the leading center for purple dye production. Murex dye had “great brilliance and fastness in comparison with other known dye”. These qualities, as well as its great expense, resulted in the murex dye being associated exclusively with royalty and the governing class. It was arguably the most famous dye of antiquity.
The work goes on to cite many historical artifacts and works which connect the Murex snail with the color purple.
On page 87 of that work, the author addresses the question of "Why is it that the Murex snail is often cited as the source for purple dye?" Several points are raised, including that according to historical sources, (1) the snail could be used to create both colors, (2) "hycinthina," the color forbidden for non-royal use, is the same word used by the Septuagint as a translation of "תכלת," among other reasons.
The "bottom line" of that discussion (p 90):
Bottom Line: There is much mention of the Murex being used as a blue dye, although purple was more popular for Roman royalty. Furthermore, “blue” was likely included in the ancient term “purple”.
On page 90, you will find the discussion of the question "Perhaps the violet-purple dye that can be produced from the Murex is really the ארגמן dye that is mentioned several times in the Torah?"
The response to that question is that according to medieval commentators (Rambam, among others), the color ארגמן is actually red. Some compare the color of ארגמן to תולעת שני, which is often translated as "scarlet."
That said, Philo and Josephus were cited as claiming that ארגמן is derived from a different animal: πορφύρα – porfύra (the purphura snail).
The "bottom line" of that discussion (p 92):
Bottom Line: According to the Rishonim, ארגמן was a red-dye derived from an insect. According to others it was derived from a sea creature – probably the Murex Brandaris that was recorded as the source of redpurple in those times.