I'm in contact with the developer of the New Computer Modern font
because I asked him to add support for stacked diacritics in his font.
After various tests and fixes he was able to make diacritics that stack properly when the font is viewed in FontForge, but the LaTeX output still has some rendering issues, so we believe that they are caused by bugs in the compiler. I attach two pdfs, one containing the XeLaTeX's output, one containing LuaLaTeX's output for comparison, and I attach the source file as well.
I would like to emphasize some test result:
These tests were made on TeXLive 2020 for Windows, updated on 2021-03-19.
Thank you for your attention.
Anonymous
Update: there was a bit of confusion about character U+0315 and its behavior, so ignore the results of test 10, 11 and 12 for New Computer Modern; XeLaTeX is working properly because Times shows the proper behavior of the diacritic in these tests.
Update 2: Antonis Tsolomitis recently uploaded a new version of New Computer Modern, which contains the stacking diacritics, to the CTAN. If you want to reproduce the bug, use those fonts instead of the one contained in mwe.zip.