Ahhh.... melamine-faced particle board. Always difficult. Having paper-tape on the cutting (face side) and a saw that only cuts on the down stroke (there's a lot of double-cut saws out there that cut on the return too, nasty things).
The only other successful method I have found is to use a fine-toothed circular saw with the depth set so the teeth only just break through on the face side and cut from the back. Or cut it on a table saw set similarly.
We all feel your pain.