Tg does not change with load.

HDT does, kind of, but that’s already covered by the load being defined for the various conditions. HDT is always defined at a specific load so it also does not change with load (since load is fixed).

Isn't Tg a poorly defined metric? It seems like thermoplastics will lose their strength as temperature goes up and there's no abrupt transition where there's a near step-change in behavior

Tg changes? Or do you mean they deflect sooner under more load?