Unfortunately, there is not a way to do what you are asking that is built-in to the gmail interface. And you are correct regarding the two different configuration options not working in conjunction with one another; indeed they do not.
While I'm not aware of a third party app or add-on that offers this additional functionality, it could be possible to produce this functionality with Google Apps Script, or perhaps something similar to what you would like. You might check for Google add-ons, browser extensions, or other third party solutions like the ones found in "Google Play Store" and "Microsoft Store" as even some of those MS apps do interface with gmail to some extent and might provide the functionality that you're looking for. If you don't see something today in one of those areas, there could be one tomorrow so keep checking back.
Also, keep in mind that gmail is very robust and offers many features and when configured in different ways can often produce behaviors which might allow you to produce the same results as it would have were the controls you're asking about a functional part of the interface. Ask yourself what would be achieved if the function was there, the end result and what purpose it would serve, and if you look at the features gmail does have the chances are good that the same result or very close to it can be produced with what's available. Using labels and firing filters based on certain triggers can probably produce the same results and mainly with some minor cosmetic differences. But for the purpose of functionality, ultimately the same result can be achieved. There's a bit of overhead in creating the filters and the labels, but once you have the system setup, automation handles the rest.
PS: Sorry it took me five years to get around to answering this question, I just joined this forum a day or two ago.