Slavery is bad, but it's not no-cost. At the very least you have to feed the enslaved and also give them the bare minimum of care, if only to protect your investment. And then there are the societal costs of enforcement.
I would submit that any Roman farmer or businessman relying on slave labor would be overjoyed to purchase any device that would cut the need for slaves in half. (Or even by 10-20%.)
A device that cuts manual labor only does so for a single purpose. A Roman farm would have grain fields, livestock, and orchards. Slaves on the farm could do all of the jobs the farm required. A harvesting gin of some sort would only reduce the labor needs for a small portion of the farm's output.
For mechanization to reduce manual labor on Roman farms they would need to switch to monoculture crops of a type that were conducive to mechanization. It would take machines being extremely cheap to beat Roman slave labor where conquests of neighboring territories were constantly bringing in new slaves.
That implies that other kinds of landholding did not have access to cheap labor - but serf, sharecroppers, and farm hands are all pretty cheap under the right circumstances.
More pertinently, the "expensive" farm workers of the industrializing countries weren't expensive enough for farming to be mechanized until the 20th century. Second half of that before it had replaced manual forms of farming entirely. Farming itself never was the driver for industrialization, but a rather late profiteer of it. It follows that farm slaves couldn't have been the blocker for industrialization, at least not as directly as you assume.
I would submit that any Roman farmer or businessman relying on slave labor would be overjoyed to purchase any device that would cut the need for slaves in half. (Or even by 10-20%.)