I do think you might be best off working with an immigration lawyer to help put together a strong H&C application.My brother is in canada too. He is on a WP but applied for PR already. My parents are on SUPERVISA. However, I want to live my remaining life with my parents closure to me and my child. I want peace of mind with their medical expenses too. Rightnow, they are not getting any health care support.
You have the BIOS argument. It also sounds like your parents only have two children (both of which are in Canada) which should work in your favour. However I think you want to put forward additional arguments for whey they should be approved under H&C. Wanting them to get health care coverage is not an H&C argument. So this is why I think you may be best off working with a lawyer to help you form a strong case.
As I believe someone else here mentioned, it's quite possible the H&C application will take around 2 years to process during which time your parents will still not have access to health care support. So you want to make sure you keep their private insurance active for this period. Once your parents submit the H&C application, they will need to remain in Canada without leaving.
Good luck.