mackania, just enter the downs in the order presented - eg 2 down has 4 clues, enter them in order in column 2. Just leave out all vowels.
In fact it is quite possible to fill the entire grid just by cold solving the downs, most of which are pretty basic clues,
The question then is do you have the appetite to tease out the names of a bunch of obscure composers from the consonants in their names, and wordplay-only clues? Of the first 14 composers I found I had heard of exactly one. Of course, I never listen to classical music. Why couldn't it be rock guitarists of the 70s?