This is a wonderful read. Seriously impressive employment of the scientific method (the way it should be). The take-home message is probably: identify (and, if necessary, test) all of your assumptions. In this case, it was assumed that the different batches of material melted to become the same liquid, since that is pretty much how everything else melts (although that may be open to a new look now). On that assumption, the problem was intractable.

The problem was solved by someone questioning that assumption and finding out that, in fact, different samples melted to become different liquids. Once over that hump, clever application of basic chemistry principles got the rest out. Lovely work.