I clearly stated you would not get the heading
I understand all the wrinkles, but assuming constant heading and some assumption about cruise speed, you will actually get a track/position. (Actually 2 in most cases).
If the circles are relatively close together in time, it is flying north (or Sth, depending on the circles), if they are wide apart (or don't change) then it is flying E or W. Anything in between can be worked out with some assumption about cruise speed, possibly even without, I'll have to think about it.
[Not a great example, sort of assumes the satellite is sitting over the pole, which it isn't but it does not really change the viability. Also noted OldOberon post which I failed to credit and should have.]