You've probably already thought of this, but the "movement budget" could maintain a residue - e.g. your first diagonal would take 1.4 or 1.5 "moves" (so you'd need speed 2+), your second diagonal in a turn would use the leftover (so you'd only need speed 3+), etc.
There'd still be edge cases around e.g. difficult terrain or talents that consider "standard move" and "boost" movement differently, I admit, but those ought to be pretty minor?