As someone who has spent 20 years working inside the walls, suicide watch very rarely lasts more than a few days after the actual attempt, then the prisoner is returned to population. The specialized observation cells are not usually "fish bowls", they're just cells stripped of everything but a concrete slab, mattress, and a toilet. Often there's a camera in the cell monitored from the officer's station.

General population prisoners are allowed out of their cells for hours at a time. The notion that a cellmate would have been there to prevent a suicide is a red herring. If anything, the other prisoner would have left him plenty of space to do whatever he wanted, likely knowing who he was, and might have egged him on.

Prisoners have standard oxford shoes with shoelaces. Even without those- they have bedding. A sheet tied to the window bars or the bunk makes a noose. I've even seen prisoners who ripped up mattresses or tore their suicide-prevention garments up to make threads for hanging attempts.

It takes 3-5 minutes for brain death once blood flow is cut off. Rounds are made every 30 minutes in the Michigan prison system. Even if the Federal system is different, still, do the math.