well I did tell him that the airside hotel is a good backup option!

To summarize/state things differently:

If you want to stay in the airport (aka 'airside'), you can do that without any visa arrangements. You can eat and drink basically all you can in the F lounge. Technically you can also sleep and shower there, but that's not recommended (there was a recent thread on this); instead book the airport hotel. The airport hotel is airside and is located near the gates and lounges.

You can also get an entry visa - either (a) in advance, through an organizer (such as Marhaba Services or the hotel you are staying at), or (b) try your luck applying for a visa at the airport, with F lounge + airport hotel as a fallback option so your vacation wouldn't be ruined.

The 96-hour transit visa for the UAE is not a UK/Schengen style 'Airport transit visa', it is really a stopover visa.

This isn't going to be a problem. Dozens/hundreds of people arrive in Dubai on similar long transit itineraries every day and get transit visas issued on arrival. Just go to the Marhaba desk when you land and they will sponsor you a visa upon purchase of an overpriced crappy hotel room from them. Done it myself multiple times before I was resident here and know people who have done it just last week.

Mmmmm... What if I don't want to stay at a crappy hotel? My friends, my partner and I have already booked Grand Hyatt for the layover. I am the issue since I am the only non-US citizen. Could I just pay for the cheapest hotel & stay at the better hotel?

Exactly.