"more suddenly" is correct and usable in written English.
It is used to emphasize how quickly something happened. For example: "The fire spread more suddenly than anyone had expected."
The throttle reacts more suddenly.
Elsewhere, the flooding came more suddenly and with little warning.
I couldn't have been more suddenly awake if someone had applied a defibrillator to my chest.
And nowhere did popular anger arise more suddenly than in Vladicin Han.
The industry sued Napster and won, and it collapsed even more suddenly than it had arisen.
"We need a little less Forever 21 and a little more Suddenly 42," Poehler groans.
In the attempt to find fathers, daughters and friends, Victorian mores suddenly seemed irrelevant.
But Apple kept at it and I began using Macs more and, suddenly, splat, Archos was dead to me.
"Some gallery I was showing with freaked out and was like, 'You have to stop doing this, because people don't take you seriously any more.' Suddenly I was this dumb bitch because I was showing my ass in pictures".
He thinks some more, and suddenly the lightbulb grows very bright, the light pulsates, and Grampy shouts, "Ahhhh!
We talked a bit more, and suddenly he shouted, "Red-tailed hawk!" and everyone lifted their binoculars in unison.
