Having had fallen asleep

When I am referring to something that has occurred yesterday evening as I was falling asleep (continuous action, it took place while I was falling asleep), but it is no longer occurring and I am no longer falling asleep nor asleep, is it alright to use "having had fallen asleep"? It seemed correct when I used it, but I am having doubts now since it sounds so shabby.
Thanks!

to specify the sentence: "It’s still healthier than my having had fallen asleep to this. [a link to an online debate]"

P.S.: I did try to look it up, but I am still uncertain.