Did you read the article at the link I posted earlier? What is it about the possible explanations there that you find unsatisfactory?
This is the one that seems most reasonable to me:
“the lectures affirm that God the Son has a flesh-and-bones body, humanlike in form, while God the Father has a spirit body, also humanlike in form. As mentioned, Joseph later knew that the Father, as well as the Son, has a glorious, incorruptible body of flesh and bone. No doubt, his understanding of the mode of the Father’s embodiment was enlarged and refined as he continued to receive and reflect on revelation.”
en.fairmormon.org/Mormonism_and_the_nature_of_God/God_is_a_Spirit/Lecture_of_Faith_5_teaches_the_Father_is_%22a_personage_of_spirit%22
Another article, link below, also says there are a couple of possible understandings for Joseph Smith’s saying that God is a personage of spirit, and goes into a bit of detail about the options.
“We cannot avoid the possible conclusion that Joseph Smith simply did not understand the corporeal or physical nature of God at the time the Lectures on Faith were delivered in the winter of 1834–35. His knowledge of things—like that of all men and women—was often incremental, and his development in understanding was thereby accomplished in “line upon line” fashion. . . A second possibility is that Joseph Smith did indeed understand that God has a body but that the passage in Lecture 5 under consideration has simply been misunderstood.”
rsc.byu.edu/archived/lectures-faith-historical-perspective/discussion-lecture-5-supreme-power-over-all-things-do
I haven’t seen evidence of the “desperation” among LDS apologists that you mention, and I fail to see how this is an “issue” or problem for Mormons. I certainly don’t remember its being an issue or concern when I was a member.
What is the significance of the “personage of spirit” statement for you?