Maybe you can limit what BB logs? I know we deactivated at least chat logs on another server. That's what it logs:
BLOCK_BROKEN (0) - A block that is destroyed (includes liquid picked up by a bucket)
BLOCK_PLACED (1) - A block that is placed (includes liquid placed by a bucket)
DESTROY_SIGN_TEXT (2) - A sign that was destroyed and had text
TELEPORT (3) - When a user teleports
DELTA_CHEST (4) - The chest that got its contents modified (currently only fires when destroying a chest)
COMMAND (5) - When the user uses a command
CHAT (6) - When a user chats. How pleasant
DISCONNECT (7) - When a user disconnects.
LOGIN (
- When a user logs in
DOOR_OPEN (9) - Doors that were opened
BUTTON_PRESS (10) - The button that got pressed
LEVER_SWITCH (11) - The lever that got switched
CREATE_SIGN_TEXT (12) - A Sign that has new text (Not yet implemented)
LEAF_DECAY (13) - A leaf that decayed (Currently logged as player "Environment")
FLINT_AND_STEEL (14) - Blocks that a player used flint and steel against
TNT_EXPLOSION (15) - Blocks destroyed by TNT going off (Currently logged as player "Environment")
CREEPER_EXPLOSION (16) - Blocks destroyed by Creepers blowing up (Logged as "Environment")
MISC_EXPLOSION (17) - Miscellaneous explosions... Who knows?
OPEN_CHEST (18) - A chest that was opened by a player
Maybe log only placed and destroyed blocks? Possibly TNT explosions, but I think you can discard the rest until you know it working properly again? That way you limit the load created by BB.