Okay I know the op is satisfied with all your answers, but I think someone forgot to mention that when you do the spy mission "Shogun Forge Claims on Daimyo" or whatever it is called, and I believe you have to get CAUGHT, you instantly lose 10 shogun influence. So if you pause the game, have a good chunk of cash saved up, and don't have high spy efficiency you then try 3 or 4 times getting caught hopefully 3 times then you can declare war before the month ends. Although what other people said to do is much faster then to force others to give up their lands.
No, the influence drop of ten only depends on the success of the spy mission, for which reason it becomes important to hire ninjas. The infamy strike you receive, however, depends on possibility of discovery. If discovered, the infamy penalty is 8. If you are undiscovered, it is 5. The penalty for undiscovered success might have been possible to modify, but I'm not sure.
EDIT: Failure, discovered: no claim, 0 influence drop, 3 infamy
Failure, not discovered: no claim, 0 influence drop, 0 infamy
Success, discovered: claim, 10 influence drop, 8 infamy
Success, not discovered: claim, 10 influence drop, 5 infamy
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