It's looking like I may have incorrectly cited the root 'to rejoice' as *[ḫdʔ] when it may really be *[ḫdw]. I just found the cognate in Ugaritic ḫdw online. However, the exact phonetic nature of the last so-called 'weak' consonant of this triliteral doesn't affect my conjecture that PIE *mad- may be from a contraction of Mid IE (MIE) *maxéda- to explain away the origin of *-a- here (i.e. through voicing and disappearance of laryngeal during Syncope) and that it may ultimately be borrowed from the passive participle of this Semitic root. So instead of what I wrote before (*mu-haddiʔ-u), it probably should be *mu-ḫaddiw-u (Akkadian muḫaddū) which would still end up in MIE as *maxéda- anyway. So I'm still sticking with it for now.
Like I stressed before, I realize this is just a tentative conjecture but it's not a random conjecture. The brainstorming ideas that I blog about should be understood within the context of two of my observations about long-range linguistics: a) that Nostraticists need to focus on more recent loans first before reconstructing Proto-Nostratic roots blindly, and b) that conservative IEists need to get it through their stubborn noodles that PIE didn't evolve in a bubble but was most definitely affected by neighbouring languages in a much more extensive way than is currently stated in textbooks. We need to figure out exactly what happened instead of chalking it up to 'a mystery'. (I have more contemplations about Semitic loans in MIE in the near future that I need to get off my chest and I want to tackle the borrowing hierarchy mentioned in Elsik/Matras, Markedness and Language Change: The Romani Sample (2006), p.320 which I cited in Borrowing copulas - Never say never because there are more tasty connections I've noticed between Indo-European & Semitic that tie into this model nicely.)