Hi, suzaroo!

I signed on here just to answer you. I was so sorry to read both your dad and you are going through this long and tough life change. Sorry I don't have any specific advice.
My only idea is, is your dad on an anti-depressant? If so, is it one of those that are found to specifically help obsessive-compulsives? If not, it might be worth considering. I understand nowadays in general (though I'm not sure about with Alz.), hoarding is considered a type of obsessive-compulsive disorder and needs to be taken seriously and treated as a mental illness, such as with medication and therapy where the hoarder develops the ability to make different decisions with "stuff." They learn the real reasons why they hoard and what the objects mean to them that is not rational. I read where one hoarder said when he saw certain items abandoned in the street, he felt like they had to be rescued. (I thought that was quite poignant, don't you?) Many hoarders have child abuse in their background, apparently.
Of course where Alzheimer or other dementias are involved and THEN hoarding starts after that -- then I'm not sure the above applies. But maybe it would still make since --?? As we age, even without dementia we lose so much. Our youthful appearance and physical strengths, our hearing, vision, reflexes. Our loved ones and friends die, we have divorces or other losses and disappointments. If your dad is retired, he surely lost a lot then -- a place where he belonged every day and his skills were needed and respected, built-in socializing and the security of a routine, etc. He has also lost much of his independence, such as having to give up driving which I'm sure is a very unwelcome blow esp. to a man.
And I feel we even lose the basic respect or regard of much of society as we age. My elderly father was upset recently when a doctor said something about a health problem my dad had, which the doctor said offhandedly looked pretty good "for someone his age."

My dad felt "written off" -- he wanted the best care for his condition just like anyone younger, the best possible treatment, period.
Anyway, now your dad is losing control of his bodily functions. And no doubt he thinks about the future where maybe soon he will lose his very life in a difficult manner, becoming unable to talk, communicate or digest food.
My point is -- sorry to be so long-winded :-) -- with all these LOSSES, maybe your dad's hoarding is a way of hanging on to what little he can, the paper cups and diapers and what not, at least he can try to make sure SOMETHING won't be taken.
As far as the diaper hoarding -- I just thought, could you label the diapers by writing on each package (in big letters for him) Monday 11-3, Tuesday 11-4, etc. Then lay out the whole next week's supply somewhere he can see them and promise him you will bring more each week way "so there will never be any chance you can run out."
If he is not able to be rational enough for such reassurance to help, maybe a mild anti-anxiety medication like Ativan or one of those would put his mind more at ease.
Just so sorry your Dad and you are going through this. There are many kind and smart people on this forum who I'm sure will come in soon with practical and encouraging advice "from the Alzheimer trenches." Hang in there -- you most definitely are not alone as we all age and try to cope with these problems.