I can tell you that it will be of no help to offer to sponsor the medical costs yourself. They don't take that into account.
Have you had a look through previous cases heard by the residence review board? I think that is the next step.
Was your son included on the work to residence visa or was he too young or not born at that point? I'm asking because I was told that they use the same criteria for work to residence as for residence itself, so I'm surprised you got WTR but not residence. Otherwise can you apply for a different type of visa for him? We went the temporary route and applied for a long-term visitor visa for my daughter.