Hilbert's Grand Hotel can absolutely hold Sysiphus and his boulder, just move everyone two rooms up.
Theseus' ship is only paradoxical on the faulty premise that the ship existed in the first place.
Hilbert's Grand Hotel can manage an infinite number of boulders, each containing an infinite number of Sisyphuses (Sisyphi? Sisyphes? Sisyphodes?) by designating each boulder a prime number and each Sisyphus a counting number, and multiplying the two to get their room number.
This leaves some rooms open for additional guests, which may get management angry about underutilized rooms. There are other configurations that pack everyone in more tightly.
His happiness depends on whether or not a radioactive substance in a box has decayed, which has a 50% chance. But since it has not been observed, he is in a superposition of happy and unhappy.
Personally I'd love to be the subject of a philosophical problem so I'd say he's probably pretty stoked
"the ultimate answer to life, the universe, and everything is… 42!"
there is no reason to assume this is not relevant for this case too
