Hi,
Most likely hospital then is Greenock Royal Infirmary, Duncan Street. Possibly though, the fever/infectious diseases hospital (called Gateside in the 60s) might be the one, though don't know what the address would be. This was out in the country rather than in the town, so a better choice if he was recovering. However, if it was acute, then Duncan Street would have been the one.
If you are thinking of going west, make an appointment with registrar to see original book - details might be clearer. And before that, take a trip to the cemetery and ask the staff at the office there (up beside the crematorium) if they can give you the burial details. This might help confirm the address and/or cause of death. And, if he was not normally resident in the area, the relationship of the lair owner would be interesting.
A trip on a Thursday or Friday will also let you fit in a visit to the Mitchell to see the medical archivist, though suggest you contact them in advance to order information if they have any.
Although there is a Res address given, this might have been a lodging house while he was waiting for his boat and where he took ill. Maybe someone can tell you if there are voter's rolls available, and you could check those too.
It may have been that George was told he was dying or likely to, and therefore provided the information which appears on his death certificate. If he was a businessman, he would have to contact his employer or employees. It may also be that he carried his birth certificate with him as he was travelling: when did passports become the norm? though the knowledge of his two marriages, and particularly his divorce would have to have been passed on, possibly as next of kin on the hospital admission information. How soon after the death was it registered? If that day or next, info obviously ready to hand. If a bit linger, they might have had to track it down.
