You can't get the gold by using Stomp, not unless you mod the game. But running should do the trick, with or without Tornado Sprint.
I've gotten gold with it using only Stomp. It's tough but certainly doable.
It's very possible and not that difficult.
My approach is sprint briefly, tap jump then immediately use stomp.
You can do a stomp about every 2 seconds and the short sprint/jump allows you to cover a fair bit of ground raking in the combos.
This approach helped me play the game without being forced to get tornade sprint (I genuinely dislike it with a passion).
You're good then, I barely managed to get the bronze using Stomp, until I realized I could just run and beat it in less than ten seconds... literally...