We care too much around here and know that you can't afford to do this project twice, so we don't want to condone any sort of method for building an expensive tile floor over such an incompatible product.
Methods of building solid, long-lasting tiled floors has been exhaustively tested. Particle board and tiled floors don't get along. If a manufacturer could come up with a viable, long-lasting solution for tiling over inferior substrates like particle board, they'd make tons of cash.
Swap out the PB or choose a different material. Perhaps DuraCeramic