Military flight paths often make no sense from an observer. They're planned in advance to meet whatever needs either operational or training that the squadron or larger command unit needs to meet. We can't expect that every time a plane takes flight for the military that it has meaning beyond peacetime operations.

If you saw the E-6B flight path earlier today over the Gulf (forgot to turn off transponder) it would look like they were looking for something. In reality they were likely doing routine EAM messaging via VLF as part of standard ops. Their real mission is a lifeline to the nuclear subs for the joint chiefs, but when not at nuclear war, much of their work is "practice" to keep them proficient and the systems exercised.

Don't know if that made sense, but it's difficult to read into flight patterns like the E-4Bs have taken and derive any meaning from them.