What happens when a creature with Racial Hit Dice changes creature type?

The specific example I’m working with is a creature with RHD who takes the Human Heritage feat… and then advances by HD.

The creature retains all the traits of its previous type (so far so good), but what happens to its existing RHD? Do they change to the new type, or stay the same? The SRD says:

…but most templates that change Hit Dice change only the creature’s original HD and leave class Hit Dice unchanged.

However, this is in the context of whether class HD change when there is already an HD change happening, so I don’t know if it should generalize to "HD changing is the default".

If the creature then advances by gaining more HD, I assume that all the new HD would be of the new type, but I’m open to peoples’ opinions on this as well.

Bridging the two questions, there’s also an argument to be made that since Human Heritage is a 1st level only feat, all RHD are acquired after it is taken, and should thus be of the Humanoid type.