The past continuous of "to head" is "was heading."
If you say, "He headed to the store," that doesn't by itself imply a continuous act. He obviously is no longer heading to the store. Even when you say it, it doesn't even mean that process continued until he got to the store. He may not have gotten to the store. It merely means that in a single completed action, he pointed himself in the direction of the store. It is no more continuous than saying, "He ran to the store." You may envision him running to the store, but that doesn't make it past continuous.
Your update with example sentences only employs the simple past tense in the second example. You're using the present tense "am" with a past participle in the first and the pluperfect "had been" in the third.
Tense aside, how are these different than other similar configurations using other verbs?
They aren't different.
As for the difference between the first and second sentences in each example, whereas they can often be used to describe the same situation, there is nuance that can arise due to the active voice and the passive voice. For example:
I am headed to the store.
The above may be the passive voice. It may indicate that your present circumstance isn't of your own doing. With this, you are not committing to the fact that you headed yourself to the store. Someone else may have set you on that course.
I am heading to the store.
This is the active voice. It connotes your involvement in the act of heading. Maybe you had been headed to the store by someone else, but you yourself are continuing to head to the store now. You are an active player in your heading.