It is generally hard to get even two organisations with considerably different national perspectives to agree on a design, as evidenced by any number of Anglo-French and Franco German equipment projects which speared in because, notwithstanding all the joint statements and political fudge, fundamental national requirements were incompatible. Trying a threesome on a new design SSN sounds pretty high risk to me, especially where one partner has limited experience of SSK design and none of SSN design. It will get even more difficult, and very expensive if there are a lot of RAN specific differences needed.
Even so, SSN(R) still looks to be the least bad bet to me. It is the only approach that will deal with the shortage of current capacity in in US and UK, it has a reactor design that, once complete, can be manufactured and is in a timeframe practical for all partners. It leaves the RAN with a life problem for the Collins boats, perhaps. That is somewhat easier to deal with.
N