How can I modify a flooring transition so that perfectly fits the two surfaces?
Sure it is. This most commonly occurs between rooms, so the "door threshold" is often tasked with the job. In most cases it simply adds a third level slightly above both - depending on the design it may overlap, or it may emerge vertically (overlap is better for lousy workmanship - emerging vertically requires that the flooring end or be cut precisely, or it looks sloppy.)

An honest and substantial threshold looks 9 times better than a chintzy narrow piece of aluminum or plastic trim where someone chose to run two types of flooring together and not consider the transition; but that's an opinion (mine.)

For your "calibrated transition" make it from wood as an overlap, and cut the rabbet on the high side deeper (think about it until that makes sense.)

The "vertical" type is most commonly seen as marble or granite thresholds anywhere from 2" to 6" or more wide. Cut out the appropriate section of floor precisely, plunk in some mortar, check the height, add or remove mortar, fine adjust with a rubber mallet, let the mortar set.