You might try using a shinto saw plane (also called a shinto rasp) to rough in the angle and finish with your plane and sand paper.

Have you tried holding your block plane at an angle? This often works to allow you to plane across end grain, so it should work in this case. At the thickness you are working with, you might try using a card scraper. I mention this tool a lot in these blogs but they are versatile and you can have four sharpened edges to use, rather than just one. I've used them in similar applications.