I recently had a similar problem with a piece of a wood called cumaru, wich is extremely hard. The main problem wasn´t that the plane didn´t cut: it was the MASSIVE amount of reverse grain and tear out I had to deal with. In an area of 0.5m of wood, I oftenly had to change the direction of planing, even with my planes cutting really well.
The solution came from my father in law.He suggested me to use a tooth planed iron. Have you ever tried it? After several passes with it, using my planes on the wood was like cutting butter with a hot knife. It´s true that you spend more time by doing this, but it´s worth it. Also I keep the cap iron as close as possible to the iron (1mm may be) and as mentioned in other reply here, I would try to plane in many directions: diagonal, etc, to achieve the final result.
Hope you have fun and resolve the issue!