Fonts with well-behaved stacking diacritics?

This is definitely a font problem. As you note, the fonts designed specifically for linguistics applications (Brill and the SIL fonts) are the best at dealing with diacritic stacking, but they all have limitations of their own (e.g., Charis SIL is the only SIL font with true bold, italic, and small caps, but it doesn't have OpenType ligatures like Linux Libertine O does).

I don't know of a font list that specifically considers diacritic stacking, but I did some trial and error of my own when writing this answer, so there are a few more fonts listed and illustrated there.