Here's the entire history of Stomp on the Thwomp, and the main discoveries that removed A presses (as far as I can tell from glancing at each video's description):

17 Sep 2013: 9x
10 Jul 2014: 8x (bloated bob-omb glitch to get onto the walkway from the cage)
9 Mar 2015: 7x (star dance clip to get up to the pole platform)
31 Dec 2015: 6x (pedro spot within the cogs if the clock parts are frozen)
6 Nov 2016: 6x v2 (pendulum manipulation for moving)
15 Oct 2017: 6x v3 (pause buffered hitstun)
28 Oct 2017: 5x (jump straight from the pedro spot to the thwomp)
14 Oct 2018: 3x (cog misalignment, hyper speed grinding method, pedro spot on top of the pendulum box)
20 Oct 2018: 2x (conserve vertical speed achieved from the pedro spot onto the rotating hand)