As best I can tell, it's sort of synergistic with the need for more time for this or that evolutionary development to occur. The dates are always shifting, further and further back.
History contradicts your analysis.
In fact, although having at that point no way to determine a definite age, geologists had begun to recognize that the earth was extremely ancient (potentially hundreds of millions of years) before Darwin ever proposed, or even formulated, his evolutionary views.
OTOH, after Darwin proposed his theories, contemporary scientists published various calculations -- based on assumptions either as to how long the sun could have continued to burn, or as to how long it would have taken for the earth to cool to its present temperature assuming it began as a molten mass -- which vastly lowered the upper limit for the earth's age, reducing it from hundreds of millions of years or more, to tens of millions or less, in some cases very much less.
Of course these calculations were wrong. They assumed that the sun burned by chemical energy, and that there was no internal source of heat generation in the earth's rocks. But since no one could then imagine thermonuclear fusion, which powers the sun, or radioactive nuclear decay, which heats the earth; no one could show how they were wrong at the time.
So the dates actually shifted in the opposite direction from what you assume. (Granted, however, that geologists did continue to point to evidence from their discipline that the earth was extremely ancient, but without, prior to the discovery of new nuclear phenomena, being able to resolve the apparent contradiction with physics.)
Since geologists were finally able to establish a definite age for the earth -- with the development of radiometric dating techniques in the 1950's -- there has been no appreciable "shifting" of the earth's age. The determined figure has remained steady for more than half a century now.