While the ice at the poles continues to melt at pace, allowing the ground there to rise up, sinking the equator, so thereby driving a faster spin to conserve momentum, it is overpowering the slowing effect of the moon's tidal drag.
And that's what's so jaw dropping about it. Humans are now imparting more force on the planet than the Moon is!
From TFA
Earth’s speeding up because its hot liquid core — “a large ball of molten fluid” — acts in unpredictable ways, with eddies and flows that vary, Agnew said.
Agnew said the core has been triggering a speedup for about 50 years, but rapid melting of ice at the poles since 1990 masked that effect. Melting ice shifts Earth’s mass from the poles to the bulging center, which slows the rotation much like a spinning ice skater slows when extending their arms out to their sides, he said.
This makes sense because when the ice melts there is no significant change in local pressure since gravity stays the same and the total deformation is small compared to the mass moment water moving (generally) toward the equator. Think of it like the way ice floating and melting does not change the water level. It’s the core that’s speeding things up and the water moving toward the equator causes, largely by human caused climate change, was subtracting off that increase. The moon only subtracts 0.0023 seconds per century while the water moving toward the poles is far higher so you are correct we are having a larger effect than the moon, but just a bit differently from your description.