Did some brainstorming over the night:
The goal is to use your attack time increases, Chris, but to make them more defined and appropriate. Also, to find a reason as to why attacking on your own would cause this time increase, but not on defense or with other armadas.
The concept I came up with was supplies. The idea is that attacking by yourself would cause you, as dictator, to consume time to find supplies to engage in combat. This would be a flat time fee. It would only occur on solitary offensive combat, because with armadas they already have invisible supply chains (similarly with defense). As you take more planets and fear rises, supplies become even more difficult to find. Optionally, there could be Hydra only technology to lower the fee. Further optionally, any race with neutral or above influence would reduce this fee as well.
The concept would never brought it up in Federation mode, because the player is a mercenary and thus has numerous contacts for supply.
The fee could start small, like half a month, but would stack with each level of fear. This would give me freedom to do early raids, but make it impossible to raid everyone.