Actually, the "leading and trailing silent blocks" function has nothing to do with music being in the gaps between tracks. But it is correct that you should make sure that option is un-checked, ie, off.
If I am understanding your situation correctly (I hope) then Exact Audio Copy will solve your problems. EAC takes some setting up, and it's hard at first. But it's worth it, in my opinion.
This "negative time" is actually called the "pre-track gap."
Exact Audio Copy does, actually, rip that stuff by default. It only doesn't if you specifically choose not to rip it with the "Leave Out Gaps" option. Exact audio copy can add the "pre-track gap" to the end of the previous track (default behavior so when you start next track it starts where it would if you skipped to it), or add it to the beginning of the next track, which is called "append to next track."
If the very first track of the CD has music in "negative time"/pre-track gap, then you need to rip with "append gap to next track." The only problem with the default behavior can be seen here, in that the first track can have a gap before it with music in it... and if there is no previous track to add the gap to the end of it, then that gap will disappear. Otherwise, the default behavior of adding it to the end of previous track should be fine. If the very first track of the CD is the one with music in the "negative time," then EAC's default handling of gaps might make you think it wouldn't read them by default, since it can't append to previous track if there isn't one.
You should do the "Detect Gaps" function in EAC (only after you've fully and correctly configured it, though) to see how long the pre-track gaps are. If any of them are significantly longer than 2 or 3 seconds (see example below), while all the rest have extremely short "gaps," then that is probably the gap that contains the music.
This doesn't occur in only classical. In the Modest Mouse CD "The Moon and Antarctica," I noticed there was something missing between tracks 6 and 7 when I listened to my first rip of it. So I went back and ripped it with EAC, with the "append gaps to previous track," and the missing passage was there again. There had been a 30 second long "gap" between tracks 6 and 7 that contained sound instead of empty silence.
If you have any questions about these terms, please ask us. We already know Exact Audio Copy, so we might be taking for granted some terms or something that you wouldn't have been fully familiar with yet. Good luck with your CD ripping and let us know if it works.