Evidence of condition-dependent sex-allocation in regards to humans
I am not aware of any such evidence in humans but I know little about this literature. If you happen to have data showing that, then it would probably be a relatively big thing! Below is a series of comments that might be of interest.

Evidence from Hyena

The evolution of the sex-ratio variation in hyena have been quite extensively studied. This very short article (not peer-reviewed) cite a number of key papers on the subject.

Logic behind the second assumption

In case clarification is needed. The variance in fitness is indeed often higher in males than in females. The reason is that females (by definition) produce the larger gametes, the one that don't leave the body and therefore often pay a much higher cost when reproducing than males do. As such, females are the limiting factors. As a consequence, males compete a lot to access females and "good males" receive a lot of mating opportunities while "bad males" receive little mating opportunity causing the higher variance in fitness among males than among females.

Statistics

IMHO, there is a tradition of horrible statistics when dealing with human sex-ratio data. It is particularly the case as these papers are often published in journals where reviewer have little knowledge in statistics (e.g. medicine). Typically, "windowing" data is generally a very bad idea and previous papers in the field have reported very bad interpretation from data due to cherry picking specific ways to classify observations. Please be cautious in your statistical analysis!

About the post

The formulation of the hypothesis is clear enough but some sentences are misleading


  it makes "natural selection" sense for females to vary sex ratio`


This sentence sounds very wrong. You should rather say "females that are able to vary the sex-ratio among their offspring will be have a higher fitness".

Note that I said "among their offspring" because while this would cause variation in sex-ratio in the population, genotypes are selected based on their ability to vary the sex-ratio among their offspring and not in the population. In fact, any given individual, would appreciate if all the other would produce the exact opposite sex-ratio than the one they actually produce among their offspring.


  better chance of reproductive success


This sentence a little clumsy as well and should be replaced with higher fitness