Why would he even have access to the ligature.
Seriously? You really think inmates are issued cattle ropes and a hanging tree? Prisoners have hanged themselves and made escapes from bedsheets for centuries. FYI, the paper thin sheets issued for suicide watch weren't on his bed because he'd been out of suicide watch for several days. He had regular issue bedding. Even if he did have thin sheets, it easy enough to tear them into lengths and woven together to make it stronger. It doesn't take much ligature strength or height to do an erotic asphyxiation from his toilet/sink.
That said, no one has seen a cause of death from the official autopsy report. Sure, not saying the coroner wouldn't lie but how about we see what it says before going on a wild goose chase.