I'm glad to read that
Classical tracks typically do not fit well into the standard artist >> album, browsing method. Apple introduced Work and Movement tags, if your tracks are tagged with these you can browse to Additional >> Composer / Work >> Work. Here tracks will be displayed by composer, then work.

However, regarding performers, I've seen mention to Artist only (I presume it corresponds to TPE1) which is not sufficient for Classical music: also required are Ensemble/Band (TPE2) and Conductor (TPE3).
Is there support for these other two performer-related tags and would it be possible, for instance, to browse by either one of them?