It seems unlikely that this influence will in any way relate to the results of the experimentation, in terms of production of variance or difference in heritability. Yet this seems to be what you are hand-wavily suggesting, without backing it up with math.

We do know a fair bit about that. The idea is that it influences the germ line via selection.

If you perform experiments and the result is that you die - or fail to mate - the selective mechanism of information-transfer into the germ line is obvious. Milder outcomes have less dramatic effects - but still result in information transfer. The phenomenon has been studied under these names:

• Genetic_assimilation
• The Baldwin effect
• The assimilate-stretch principle

If we go as far as humans there are also things like: Biocultural evolution.

That learned information and genetic information were aspects of a more general underlying phenomenon was observed by Semon (1904) and later there were pioneering contributions by B.F.Skinner - for example in Selection by Consequences. Skinner explicitly based his theory of learning on Darwin's theory of evolution. The idea was refined further in Dennet's Tower of Generate-and-Test.