The OP has the following confusion:
(1) I'm confused about the concept of hole diffusion, ...
(2) Wouldn't it be more accurate to say that the electrons "fill" the holes in the p-type material?
(3) Would it be accurate to say that positive current in a p-n junction involves hole movement in the p-side, but when it comes to the n-side, involves "movement" of positive charge by positive ions, ...
I think the root cause of confusion is the inaccurate use of the word "move".
Let me use the musical chair game as a analogy, to explain to my 3 year old niece Jenny, how an empty space of a chair can "move", though the chairs do not "move" themselves.
Part 1 - Accurate use of the word "move"
(a) Suppose in the beginning, the 8 chairs are occupied by 6 children, leaving 2 chairs say, blue and green empty.
(b) Now the teacher Simon says, "Everybody moves one chair to the right".
(c) After much chaos, everybody indeed has moved to the right.
Now if I ask Jenny if she agrees that everybody has moved to the right, she would say yes.
Part 2 - Inaccurate use of the word "move"
Now if I then ask Jenny if the original empty chairs, blue and green, have moved to the left, she would say No, because the chairs cannot "move".
Here comes the trick question for Jenny: "But have any empty spaces moved?" She would say, yes, two empty spaces have moved.
Now if I challenge Jenny, "I know a real thing, such as a child, can move, how come an "empty space" can also move?"
She would be annoyed an replied "Why not, of course a non real thing, such as an empty space, can also move. How stupid you!"
Part 3 - How come the semiconductor physicists use the word "move" inaccurately?
Well, the semiconductor physicist Simon Sze uses the "hole" in his book on Semiconductor Physics and Technology.
By the way, the other physicist Stephen Hawkins is also very inaccurate to say that Black Hole is a "hole".
/ to continue, comments welcome.
Discussion, Conclusion, Recommendation, and Jokes
Two atoms are walking down the street, and one says to the other, "Wait, wait, we have to go back. I've lost an electron somewhere."
The second atom says, "Really? Are you sure?"
To which the first atom replies, "Yes. I'm positive."
Heard on NPR and contributed by Peter MacLean Kunhardt
/ to continue, ...
(1) Meaning is use: Wittgenstein on the limits of language - Timrayne, Philosophy For Change, 2014mar11
(2) p-n junction - Wikipedia
(3) PN Junction (Solar Cell and LED) YouTube Video - RED Inc Communication, 2014nov06, 135,696 views
(4) Semiconductor Basics - Electronics Tutorials
(5) PN Junction Theory - Electronics Tutorials
(6) PN Junction Diode - Electronics Tutorials
(7) Semiconductor Devices Physics Technology，Simon Sze 2nd Ed Wiley 2002 (free ebook)
(8) Modern Semiconductor Devices for Integrated Circuits (Ch 1 - Electronics and Holes) - Chenming Hu
(9) Modern Semiconductor Devices for Integrated Circuits (Ch 1~8) - Chenming Hu
(10) p–n junction - Wikipedia
(11) Input characteristics of NPN transistor - Khan Academy Video
(12) Parts of a transistor - Khan Academy YouTube Video
(13) Transistor Current and Parameters - Khan Academy YouTube Video
(14) PN Junction Q&A and Chat - EE SE 2020jul26
End of answer