The fruits of labor that are not accounted for in a quid pro quo transaction with capital are those that go to land, for which there can be no quid pro quo transaction because you must occupy (and labor upon) land. If there were infinite land available, labor could simply move to that land and produce what they themselves can produce from nature with no gains going to capital because they need not employ capital to survive. If there were infinite land available, the only people who would choose to employ capital (or be employed by a capitalist, same thing) are those who believe the bigger pie is worth the smaller slice.
However we do not live in a world of infinite land, and so that calculus happens^ but it is coerced by the necessity to live and work on land owned by neither labor nor capital. Given that capitalists don't work directly on land and are generally "more efficient" (this is why capital is valuable, aka this efficiency is what capital is), the world becomes separated into those above the "rent line" and those below the "rent line," and there are far more capitalists above than below and far more laborers below than above. This creates tension between labor and capital, but neither of them are getting what they produce, but that's not because capital is stealing from labor - rather land is stealing from both, just capital has greater capacity to be stolen from before descending into poverty.
In any case:
* Not every point of an ideology is mutually exclusive of every point of every competitive ideology.
* Georgism is not about socializing land nor centralizing control. It is explicitly not about that. It is about socializing the gains on land produced by external factors (nearby public and private investment, technological improvements, etc)
* You mention Georgism tends to be politically unstable. Could you point to some historical examples you have in mind?