Thanks for the feedback! Glad to hear that the problem is solved :)
Never doubted you had proper joysticks: it's Windows that treats them as analogue devices! For clarity: the sticks of joysticks are digital devices and, from a software point of view, are equivalent to D-pads; however, at times, Windows reports them as analogue thumbsticks! In fact, the solution I adopted was to accept and handle also analogue input as if it were digital. In short, the game now features a workaround to a Windows issue.