"There is an infinite hierarchy of such universes in a single Step of the Tower."
This is the part that requires a direct statement, because I've yet to come across one at any point, and to my knowledge, it is wrong.
The quotes I've seen thus far (Including the ones linked within the last few CRTs relating to this verse) describe the steps/floors of the Tower as simply being their own separate layers, where an entire universe found on one floor is contained within a single atom found on the floor above.
That's it.
"There are infinitely many Stairways."
This one is definitely wrong. There is exactly one stairway in the Tower, and it's the one we see Roland climb at the end of the series.
From the Coda of DT7: The Dark Tower:
He raised his hand as if to knock, but the door swung open of its own accord before he could touch it, revealing the bottom steps of an ascending spiral stairway. There was a sighing voice — Welcome, Roland, thee of Eld. It was the Tower's voice. This edifice was not stone at all, although it might look like stone; this was a living thing, Gan himself, likely, and the pulse he'd felt deep in his head even thousands of miles from here had always been Gan's beating life-force.
Commala, gunslinger. Commala-come-come.
And wafting out came the smell of alkali, bitter as tears. The smell of…what? What, exactly? Before he could place it the odor was gone, leaving Roland to surmise he had imagined it.
He stepped inside and the Song of the Tower, which he had always heard — even in Gilead, where it had hidden in his mother's voice as she sang him her cradle songs — finally ceased. There was another sigh. The door swung shut with a boom, but he was not left in blackness. The light that remained was that of the shining spiral windows, mixed with the glow of sunset.
Stone stairs, a passage just wide enough for one person, ascended.
"Now comes Roland," he called, and the words seemed to spiral up into infinity. "Thee at the top, hear and make me welcome if you would. If you're my enemy, know that I come unarmed and mean no ill."
He began to climb.
In fact, part of The Man In Black's speech at the end of The Gunslinger confirms both of the things I've said...
From the Coda of DT7: The Dark Tower:
"Imagine the sand of the Mohaine Desert, which you crossed to find me, and imagine a trillion universes - not worlds but universes - encapsulated in each grain of that desert; and within each universe an infinity of others. We tower over these universes from our pitiful grass vantage point; with one swing of your boot you may knock a billion billion worlds flying off into darkness, a chain never to be completed.
"Size, gunslinger... size.
"Yet suppose further. Suppose that all worlds, all universes, met at a single nexus, a single pylon, a Tower. And within it, a stairway, perhaps rising to the Godhead itself. Would you dare climb to the top, gunslinger? Could it be that somewhere above all of endless reality, there exists a room?...
"You dare not."
And in the gunslinger's mind, those words echoed: You dare not.
I'm not trying to be condescending or anything here, but these two misconceptions might be part of our problem.