There is a basic problem with framing though. Why does the labour need to find somewhere to go, but capital doesn't? Why can't the increase in productivity be captured by labour and denied to capital?

Do you mean to imply a political/social revolution? In any other scenario I can think of when my boss gets a new machine, he captures the value from my increased productivity or the machine eliminates my job entirely.

Changing the tax system to tax capital rather than labour would probably get you 90% of the way there without great societal upheaval (capital would fight back though).

Obligatory land value tax mention