Thanks for this thoughtful post, Heather. I certainly agree with your call for more thorough thinking through how to rigorously collect AND ANALYZE qualitative data, and - having organized a lot of original quantitative data collection - I'm not at all blind to the problems with quantitative data. And I certain don't privilege all quantitative analysis: I do mostly RCTs, in which I have significant confidence.
Perhaps one of the challenges is that few researchers (that I know) can effectively speak both the language of quantitative analysis and of qualitative analysis, and so there can be a tendency for each group to dismiss the other. Alternatively, the qualitative research is thrown in to complement the quantitative analysis. (I would say more than dressing up and humanizing: Also to interpret quantitative findings.) Perhaps a more productive, constructive model, would be a research team where you have a PI with expertise in quantitative analysis and a PI with expertise in qualitative analysis. As I look on some of my own recent mixed method experience, it's clear that if we have invested the same resources into our qualitative work as we did in the quantitative work, we may have gotten something much more substantive. But I'm - by training - a quantitative researcher.
I do feel like most of the issues that we have with quantitative data (e.g., people potentially lying, external validity) are just as likely in qualitative data, although I'm happy to be proven incorrect. Unfortunately the Lincoln & Guba reference you link to is Harvard-gated; it looks like a great contribution to the literature.