Yep, mighty big tips.
Here is my method for thinning tips, I call it "sighting in a bow".
I use a belt sander but any sanding block or file will work as well.
I put the fade of the opposite limb from the one I am working on my shoulder and sight down the limb like I am aiming a gun. I touch the sides of the limb tip to my belt sander and resight down the limb. My goal it to remove a little wood at a time and always center the tip with the handle and the rest of the limb. A little off one side, check, a little off the other side and recenter.
Be sure to have some measuring device handy to constantly check your tip width. What looks like 1/4" while you are reducing the tip with will actually measure around 1/2". 1/2" tips look really small when compared to what you start with before you start thinning the tips.
The reason I use the sight in method to finish tips is because no matter how carefully I lay out a stave the tips will be just a little off from center when I start tillering. Since I started visually laying out my tip position my strung bows almost always have the string centered or very close to centered over the handle.