My heart goes out to you, and your family, 1000x.
Any adult with mental issues, and/or just very poor judgment, can be very, very hard to control, financially, behaviorally, legally. Especially at this point, if they’ve never had an official diagnosis that allows such control (rare!), in most locations it’s almost impossible to get one now. Don’t know how it would work. Often the subject person has to agree to any doctor / other professional examination, and all too frequently they opt out.
That said – you didn’t mention your attorney visit, to discuss this family situation and all of your alternatives. If I knew who you are and where you are, I’d call myself and schedule you. 
This is on you. Gotta get it done. Best hourly fee you will ever spend.
I get the frustration of being given a lot of paperwork to get your dad to sign, knowing that’s an uphill battle. But you also need to hear the experienced attorney’s experience, thoughts and observations.
This is what worked with my dad, knowing that everyone, and every situation, is different. My dad was of the Korean War generation, grew up during WWII so not quite that generation, but before the Boomers. He graduated military college as a 2nd lieutenant, did 2 years in Korea, came home and married mom.
So that’s the traditional family type of framework that was his life, that meant that he was Head of the Family. Throughout his final years we continued to treat him as Head of the Family, who was being catered to with rides to the doctor, attorney consultations, special caregivers, all things being done for him, not to him. That got a lot of cooperation. Not always perfect, but he actually got better as things progressed and he was more dependent.
The other thing was never, ever getting into the weeds of “what we need to do”. As you mention with the cognitive, it no longer made sense to him. He’d divert, deflect, never ever get into what was needed.
Instead of that, do it, then bring the paperwork home for him to sign. Or, we’d take him to the attorney’s office to tell him what needed to be done, and/or sign. At first, we went to the attorney’s office and the attorney explained it – dad listened politely. To get him there I just announced “We have an appointment on [date] at [time] with the attorney [name] to review some things for the family.” Placed a note with this info on the kitchen counter. And then left to avoid a big discussion/argument! 
By the time for the appointment (I drove), he was curious and ready to go.
What dad really got out of the attorney visit was that ‘this is what Responsible Heads of Family do’. That is what impressed him, not the why’s and wherefore’s. Later when the paperwork came he was ready to sign, if the attorney was invoked.
Made it a formal occasion. “We have some papers from the attorney.” Everything cleared from the kitchen table to get this thing done, an assumption in our manner and tone that these things were necessary for the family structure, of which he was the responsible head.
Our expectations were couched, framed and contextualized, that these things that needed to be signed or done by him as the Head of the Family. It was already prepared for him so he didn’t have do to much but sign. Everyone relying on his responsible role. It worked a charm, because it fit his personality.
He’d sign anything if I sat down with him at a clear kitchen table and presented important documents (that he didn’t read) and said very formally, as if I were the attorney, “You need to sign here. OK here’s the next one, here’s where you sign.” And/or “The attorney [name that he knew and trusted] says to sign here.” Dang it worked.
If he asked “what is this for?” I’d keep it brief and high level, no details. Like getting a stack of routine signatures from a CEO. Looking down at the papers, not at him. “This will make sure that we will take care of your affairs if you can’t. Here’s where you sign.” “This is in case you are unconscious in the ER and the doctors need to talk to us. Here’s where you sign.” Sometimes I’d invoke the attorney’s name, preferencing the comment with "[Attorney name] says … "
If he wanted more explanation (rarely), I’d put the papers aside and say “Sure, let’s go talk to the attorney and he can explain.” That way it’s not me on the spot! 
My dad would almost immediately say that wasn’t needed and sign (avoiding another hourly bill from the attorney!).
If I/we tried to explain why it was important, or what it meant, he wouldn’t sign, or listen, or discuss. He’d deflect and divert, he’d say maybe later, maybe it wasn’t needed. The more words from others, the less he was into it.
I think he could no longer follow all of that. He needed things very simple and formal.
The truth is that he was a math/physics genius who had probably never fully understood the legal stuff. He had always followed his attorney’s guidance, or mom’s guidance. He thought mom was smart and actually read the complicated stuff, which was true. If she was signing, he’d sign. After mom was gone, if the attorney said so, then he would sign.
OP, your dad is likely of a different generation. But if you can make your strategy fit his own self-image, his role in the family and in society, whatever that is, it might help. And it might take different tries spaced out in time. Don’t be surprised if, at some later point, you find a window of time when he is much more compliant. As he realizes for himself the amount of his decline, and before he loses all rationality. There is no knowing how long that window of time will last.
Also: I would not just say “you need a POA”. People think they are immediately signing away all of their assets. Something like “you need a POA that only becomes effective if you aren’t able to make your own decisions, so the bills get paid and that kind of stuff”. “You need a Health Care POA that only becomes effective if you are unconscsious or something and the doctors need information.” Whatever resonates with that individual.
Keep “only becomes effective if” in the sentence. They know they need that POA. What they don’t want is something that gives away their bank accounts now, which is most people’s default assumption.
You need to get the HIPAA forms done for every medical office your dad sees, both GP and the hospital(s) within his insurance. They will not speak to the family without it, except in some emergency cases.
Good luck!! I wish there was an easier path. This is hard for every family, each in their own unique way. You aren’t alone !!! 
