So i spoke to my uncle today for you, he is a builder with 30+ years experience.
He said what i expected to a degree, he cant say for sure without seeing it, even then it is hit and miss to a degree.
He did not see any reason why it cant be done, and pointed out the countless cast iron bath's that used to be fitted to normal single joist floors with no issue, he also pointed out the most bathrooms here do not have such a large span as the room that you want to use.
He said that if it where his house, and assuming there is space in the garage underneath that he would double the joist immediately under the tank across the fullspan. Also fit a support perpendicular to the double joist close to the outer edge of the tank. This support would be held in place with what we call 'acro's' over here in order to stop sagging, which are 'temporary fitment' extendable steel support poles used for removing lintels/rsj's to support brickwork.
He pointed out that the Acro's may not be essential per say, but it is the only way that he would say for sure to be a safe bet without observing the structure in person, given the possible damage that could be caused. This advice of course is assuming that current joists are sound, and well fitted.
Personally, in my own house where i have double joisted with high quality wood that is well fitted i will not be using acro's, however, my choice of tank will not be as large as yours and i own my house outright so the risk is on me.
I think thats all the input i can really put into this now, unless you need advice on the fitting of joists and 'temporary' steel supports.
I also think you have enough information on this thread from various folk to make a decision as to what is the best idea for you and your folks home in the long run.