...was Ancalagon the Black at the fall of Gondolin?

A.  There also seem to have been some robotic dragons, per your earlier quotes on this subject.

B.  You should also note that Morgoth is specifically said to have put a powerful evil spirit into Glarung's body.  Tolkien's dragons are composite creatures, demons in reptile form.

C.  My utterly unsupported theory of the day is that a cold-drake is the unmodified stock from which the fire-drakes were derived.  Morgoth may have put spirits in a few of these before deciding that they could be upgraded.

D.  As a bonus unsupported theory I propose that the term 'drake' designates a male dragon, as it designates a male duck.  The females might be spwecifically 'worms', which is also a collective (some people might like an example of the feminine term also being the general, contra 'Man').  Hence the distinction you note is by gender, not race.

E.  Fine, but let's not pretend the list can be conclusive.  We have hints that Morgoth devised many monsters, any number of which might be more or less dragonish.

Appendix:  I take the Were-Worms of the Last Desert to be a Hobbit Fairy tale.  The Last Desert itself is almost certainly mythical.