The first thing which came to my mind after reading your description would be 'Liquid Tension Experiment' (Since '07 known as 'Liquid Trio Experiment'), a side project band from Dream Theater's drummer Mike Portnoy.
It's a mixture of rock and metal, so it actually fits half into your favourite genres, and I guess it does never hurt to take at least a look at it. Here's an
example, all their stuff is completely instrumental.
Another name which would fit into your descrption would be Warmen, a finnish melodic metal band and side project of Children of Bodom's keyboardist Janne Wirman which is also influenced by european classical music. Although I'm not sure if that's your taste, it features a lot of fast and awesome melodies. About half of their stuff is instrumental, here's another
example.