Try disabling the speed hacks and use NATIVE option in GSdx config.
Which version of pcsx2 are you using? Use v0.9.5I have "a bit" other problem - I have the native option on and well ... speed hack? Where is it? I have GSdx 846 (MSVC 15.00, SSSE3) 0.1.9 and ... I don't see it.
Well, back to the topic - during cut scenes sometimes I also have black screen (rarely and it lasts only for a brief period), but sometimes not black screen but ... moving water? It looks like the water of the Blitzball - well ... I think that the water just switches the black screen - I had it on the beggining of the game after starting playing blitzball, then after some time it vanished and it returned again after I returned to Luca (after obtaining airship) and later on playing Blitzball again (for Wakka's crest and sigil).
How can I fix it?