[The Saucepan Man]

He has the ability to create, perhaps through a twisted song or chant as the other vala do- without needed anything as a base.

He couldn't create a creature with sentience from scratch, just as Aule couldn't with the Dwarves. Although I suppose he could have created non-sentient creatures and imbued them with disembodied spirits. But I'll carry on indulging my imagination ( ) and stick with the dinosaur theory.

There is no evidence of any Dinosaur-like-reptiles

In a world containing a giant squid-like creature, Oliphaunts and the Nazgul's fell beats, I am inclined to believe in the possibility of such creatures having existed.

if they existed, the Professor would have at least hinted to them somewhere in all of his works

I would find it very surprising if there were not creatures living in those parts of Middle-earth about which we are told very little (Far Harad, for example) which Tolkien never referred too. Surely, Tolkien's works do not contain a complete catalogue of the entire flora and fauna of Middle-earth throughout the Ages.

Apart from the fact that dragons slowly diminished, and even with the numbers of those slain, if they were reproducing, the race would still survive somewhere, or even grow.

Not necessarily, if their mortality rate exceeded their rate of reproduction (Dodos reproduced, after all). Or, assuming that Dragons were not hermaphrodites, perhaps there were no females left by the end of the Third Age.