After a bit of a break I ventured onto the Ancestry site and noticed that they had ‘new’ prison hulk registers and letter books. I found that my ol’ pal, George WHITE was held on the Ganymede while awaiting trial and/or transportation to Van Diemen’s Land in 1834.
I have found reference to ANOTHER Ganymede – an iron clipper-barque built in 1868 which was hulked in 1912 (source).
Although I don’t claim superior naval knowledge, it is more likely that the Ganymede my commenters refer to as being used as a convict vessel in 1839, is a DIFFERENT ship to either of these as ship names were often REUSED.
I feel I should also add here that wikipedia was not my only source. The Index of 19th Century Naval Vessels also contained this information and I have updated my source in the post to include this link.
However, if you feel you have evidence that proves these ships are in fact the same vessel I would be really interested to hear about it.