Strategy for dealing with giant sample size
My link in the comment has useful advice. I'd like to emphasis:


This is a very well known fact in statistics
Large sample size is good. There's nothing wrong with more and better quality data.
It's silly to split up the data in your second point. You are voluntarily giving away information and statistical power. People do that for training an unbiased model, but not to reduce sample size for the p-values.
There's no reason to switch to another model. The standard error in your logistic model should be small, which makes it ideal for predictive modelling. Your model should be robust and stable.
You should do your analysis on effects size if you have a large sample. Read @Sympa's answer in the link I post. What's your magnitude of the effect size? What's the relative effects?
The threshold you have for your first point is domain specific. If you write a paper, you should know it very well. You could compare your data with the literature. Simple descriptive statistics like percentage and how it compare with the standard deviation (which is independent to sample size) would be useful.


Please also take a look at https://stats.stackexchange.com/questions/125750/sample-size-too-large.

There is a long but excellent article on Bayes factor and p-value:


  https://replicationindex.wordpress.com/2015/04/30/replacing-p-values-with-bayes-factors-a-miracle-cure-for-the-replicability-crisis-in-psychological-science/


I should draw to your attention the following paragraph:


  The more interesting argument against p-value is not that significant results in large studies are type-I errors, but that these results are practically meaningless. To make this point, statistics books often distinguish statistical significance and practical significance and warn that statistically significant results in large samples may have little practical significance. This warning was useful in the past when researchers would only report p-values (e.g., women have higher verbal intelligence than men, p &lt; .05). The p-value says nothing about the size of the effect. When only the p-value is available, it makes sense to assume that significant results in smaller samples are larger because only large effects can be significant in these samples. However, large effects can also be significant in large samples and large effects in small studies can be inflated by sampling error. Thus, the notion of practical significance is outdated and should be replaced by questions about effect sizes. Neither p-values nor Bayes-Factors provide information about the size of the effect or the practical implications of a finding.


The reviewer was correct. Neither p-value nor the bayes-factor reveals anything about the effect sizes.