On my modded d-pad it's even easier than on the stick, just press forward and then let your thumb slide from the bottom to the df-position.
While Gouken's Shin Shoryuken already does considerable damage, it should be noted that it deals significantly more damage when used by Gouken as a boss in the Arcade Mode; it is enough to deal roughly two thirds of the average fighter's health bar, requiring the player to respect the threat of the move which can completely swing a seemingly advantageous fight.
Just like the Shin Shoryuken, it has a lengthy recovery and leaves Ryu open to attack for a significant amount of time.