I have used that same selection many times with good results. The first bass pictured below is a laminated Birdseye Maple, Wenge, Purpleheart combo with a Birdseye Maple neck. I found that the tone of this bass is somewhat brighter with nice low-mid growl.
It is the biggest pieces of the body and neck that make the biggest difference in overall sound. All of the woods you have listed will have a brighter tone as they are all very hard woods.
I have recently made a bass (see the second bass below) with many of the same woods, but with a larger amount of Purpleheart, and I found that a single MM pickup did not give the bass enough bottom end. I had to add a Jazz pickup to bring out some more bass. It was because of the large amount of Purpleheart used in the body that made the bass brighter in tone. The Walnut and Maple used in the body were not a very big factor on the sound because the top pieces were not very thick. So I think that if you want more warmth in the tone of your bass with using the types of wood you listed, you may want to consider pickup placement and possibly chambering the body (if you are using a top wood) to add some roundness to the overall tone.