The question becomes one of to what extent is is no longer possible to limit workforce replacements to a small enough percentage that it's beneficial to the overall economy.
No, it doesn't. The problem isn't of how much, but how much per unit time; if the question becomes how much, implement complete and total communism, because you have entered a post-scarcity economy and everyone has so much money they can't find any way to spend it all.
We roll the dice you're stumbling over every once in a while. The last bad one was the Industrial Age, where we had 70% unemployment for 60 years; it sucked.
The last good one was the Information Age, where we replaced mostly clerks in offices managing paper document stores so large that an ever-expanding army of clerks couldn't do it--that is, you may hire 2000 clerks to handle 2000 times as many leases and contracts, but your workforce isn't going to handle the workload anyway, and your business is going to collapse under its own weight; the Information Age (computers) solved this by making it POSSIBLE to expand industries that desperately wanted to grow, not by throwing out massive numbers of jobs and then trying to make up new markets. New markets came rapidly because new jobs in existing markets showed up everywhere, and everyone got friggin' rich.
The next one is the automation age; it resembles the industrial revolution more than the information age, and will sharply create a 50%-ish drop in employment in industries which are not hitting walls trying to expand. Those industries are sized for the demand, and won't explosively grow; new jobs won't rapidly appear over night due to automation, and so the turn-over won't magic up so much wealth as to expand the middle class and create new markets out of nothing.
I think that eventually we'll reach a point where there's enough material wealth generated through automation that everyone can be given food, shelter, and clothing at no cost
Automation won't do it. The core problem is energy scarcity; we can transmute any material into any other material through energy-expensive processes, so we are capable of using millions of times more energy than we currently produce or consume. A dyson sphere completely enclosing the sun and using modern parabolic reflector sterling engines at 39% efficiency would generate 13,000 TRILLION times as much energy as we use now, and would end us into an unknown post-scarcity economy as you suggest; however, I don't project the specifics being something I can simply describe, and don't attempt to do so. It may not instantly create a utopia; it will create the economic situation prerequisite for a utopia.
As for today, a capitalist solution works. For just a hair below the cost of our current welfare system in America, we can create a capitalist feedback loop that supplies everyone food, shelter, clothing, utilities, clean water, and so forth. Any business participating in the supply side will make billions in pure profit, so somebody will do so; as for the incentive to work, I specify everyone (even Warren Buffet) gets the Dividend payment each month, and so employment carries no risk of losing welfare benefits, nor reduction in benefits, and so a job is always an improvement in your financial situation. Incentive.
Solving poverty wasn't a difficult problem.