In general, being "just about to [do something]" means that the action is in the immediate future, not already ongoing. Possible translations would be "kurz davor sein, [etwas] zu [tun]" or "gerade [etwas tun] wollen" or "im Begriff sein, [etwas] zu [tun]".
"I was just about to call you" => "Ich wollte dich gerade anrufen"
"He arrived when we were (just) about to leave" => "Er ist gekommen, als wir (gerade) gehen wollten"
In contrast, if the action was already in progress:
"He arrived when we were just saying goodbye to everyone" => "Er ist gekommen, als wir uns gerade von allen verabschiedet haben." or "Er ist gekommen, als wir gerade dabei waren, uns von allen zu verabschieden."
The difference in German is the missing "wollen" here -- they are not planning/willing to say goodbye, the are already doing it.
Likewise, your examples 3 and 4 are about something that is already in progress, so in English you cannot use "about to do sth." any more:
Er war gerade dabei abzuwaschen, als das Handy klingelte. => He was just (in progress of) doing the dishes when the cell phone rang.
Sie war gerade dabei, einen Brief zu diktieren. => She was just dictating a letter.
So in German, the difference would be between "etwas (gerade) tun wollen" (= immediately before starting to do something) und "etwas gerade tun" (= in progression). In English it would be between "to be just about to do something" and "to be just doing something".
That said, there are definitely edges cases, depending on the verb, where an action is at the same time "just about to happen" and "already happening". For example, "leaving a party" can be something that can stretch over a long time, during which it's at the same time already happening and about to happen. We are finishing our drinks, we are going around saying goodbye to everybody, we are getting our coats, thanking the host, talking at the door, before, much later, we actually leave.
So in this case, being "about to leave" and being "in progress of leaving" can be the same thing, and so can "gerade gehen wollen" und "gerade gehen". In the case of such verbs, it might be fine to translate e.g.
Er ist gekommen, als wir gerade gingen.
He arrived when we were just about to leave.