Is the grain oriented so you could use a chisel?
A big wide chisel taking shearing cuts would do it, and a huge skew might be better again.
I might make one if I need to do something that calls for it (that a router can't do)
Spring steel makes an OK chisel I've found out, probably could be improved by heat treatment
but for the odd job suffices.
A truck leaf spring might have enough meat to procure a chisel from, with plenty of grinding as they look to be around 15mm(ish) thick, if you can't obtain flat spring steel.
Keep the planes for you might need a few more.
Having a course, medium and fine plane is just not enough for me for my use.
Tom