Another option is to use your wimpy router, but not all the way
through. Even with a 2000w router, I'm not convinced it's best practice
to do it all in one cut. You could do it all with the router in about
10 passes going progressively deeper (if you can find a long enough
1/4" bit. Alternatively, you could do a shallow cut with the router
(it's the laminate you want cut neatly) and then do the rest with a
jigsaw. You could then tidy up the cut with either the router or a
rasp, or whatever. The router would have a much easier time as it's
only having to cut half the material, and the waste won't clog up and
overheat the bit.

-Antony