It looks fairly simple to get a SIM card for my iPhone in any of these places - but is there a single provider or SIM that will work in all of these places so I don't need to source a new SIM in each country? I'll be starting in HK for what it's worth, will the HK SIMs work fine in the other countries without huge roaming charges?

Don't need much - just a few minutes / texts in case of emergency and a few GB of data.