John, there are plenty of online resources for achieving the kind of finish you want. I've done some similar finishing, though not on "our" dash wood. It involved a large number of coats of rattle-can (oil base; do NOT bother with water base materials) satin polyurethane. I used Minwax because that's what was available. After doing a few light coats, I let it dry for a couple of days. (try to do this in a clean environment, and don't try this when the humidity outside is high). I then rubbed down the finish with a rottenstone compound and water. Then I repeated that at least twice. The idea is to get a very solid "base" of polyurethane for the final coat. The final coat, if you are using a satin poly, should give you the result you are seeking. Some say a final rubdown with 0000 or very fine bronze wool will further impart a more uniform satin look, but I didn't need to do this.
If you want to experiment before you start on your own wood, get some scraps of teak, walnut or whatever and experiment.