The link to the Berry, et al. paper, their links to the King, et al. (2000) paper, this post on AndrewGelman.com (http://andrewgelman.com/2015/05/04/a-causal-inference-version-of-a-statistics-problem-if-you-fit-a-regression-model-with-interactions-and-the-underlying-process-has-an-interaction-your-coefficients-wont-be-directly-interpretable/), all point to one incontrovertible conclusion: this is a highly contentious topic about which there is little agreement in the literature. For instance, Berry, et al's "compression" effects in a main effects model sounds like little more than a lack of independence among the predictors to me. After Wooldridge, you may well be better off simply testing for endogeneity in the error term rather than jumping through all of Berry, et al's, convoluted hoops.
That said, one suggestion stands out for me in terms of identifying a line of sight through the controversies: testing unrestricted and restricted models for the change in the log-likelihood. If that test is significant, then you can plausibly contend that including an interaction term substantively improves the outcome.
Of course, this is a statistical answer to the question and, pace King, et al., the challenge then becomes one of providing substantive interpretations for this result, not statistical ones. If substantive interpretations can't be provided, then perhaps it makes more sense to drop these terms from the model.
You don't provide a context for your question: is this for a dissertation, a publishable paper or an applied model such as might be used in a corporation? This is another way of asking how high the bar is being set. My point here is twofold: first, the required level of rigor changes as a function of the context. If you're doing this for a dissertation then you can motivate your choices based on a plausible but careful reading and interpretation of the literature while recognizing that there are no unambiguous, black-and-white solutions. Second, slavish adherence to a contentious and convoluted literature will do little or nothing to advance the issues. Who knows? You may achieve a breakthrough in the academy's understanding if you push the envelope.