Maybe you shouldn't limit your example-making to "sabotage", so that being sneaky doesn't cut it. You need to call people out on not being helpful (literally, tell people when you notice). You need to emphasize loyalty, and how loyalty means putting success first not their own ambitions.
So, what if every time you have any of your generals' plans fail, you go over it and look for sabotage (of course), but also try to pick out one or two places where another general could have helped, but didn't (either helping when asked or outright offering help). A failure to help another general gets noticed, officially, when the failure of said plan is announced - maybe announced privately or publicly, depending on how you want to play it. Getting mentioned for failure to help counts against you. Do so three times, and there is a public warning (which could be a punishment, whatever you want). A failure to help that might have meant the original plan succeeded, gets a warning straight off. Three warnings and your general gets made an example of, exactly the same as for sabotage - for persistent little failures to cooperate, or for direct loss of three plans.
And, on the other side - failing to ask for help also gets noticed, and discouraged. Even in a successful plan, you can be asking how help might have expended less resources, taken less effort, gained more with the same plan or resources. Not asking for help where it could have bettered the plan gets the same official notice as not giving help, with a warning for three little misses, or for one miss that might have salvaged a failing plan - and treated as sabotage if persistent unwillingness to ask for help results in three warnings.
You will have to take a crash course in general-ing, to be able to catch some of those missed opportunities... or else you might be able to get your generals to call each other out - by using a consensus of all those not involved in the plan or in a position to help, since in the beginning they will have an incentive to hit both sides, and must defend their positions to each other (to get that consensus) and to your satisfaction. And once they realize that cooperation is being rewarded, and seeming too eager to point out others' flaws may count against them in this new environment, both among their peers and to their boss - their behavior should mellow over time until you hit a level you like. You can have "spot checks" for where other generals can help a plan at any point in its development, execution, or post-plan report (which should keep people thinking about it)... so it isn't easy for generals suddenly discover lack of helpfulness afterwards to sabotage others with, without giving a good reason why they didn't notice beforehand.
So, there's no safety in "sneakily" sabotaging their rivals - they can get called out for not helping when they could have, or for giving poor help or advice, or for not asking for help when they need it - and it will entirely depend on the boss's perception (said boss will want to look especially closely at rivals when judging 'not-helpfulness' to any general's plan). The generals want to be seen as having helped others, and to be seen as having asked for help (to avoid getting warnings for their own plans). Safety comes from fewer failed plans at all - especially if successes, or maybe specifically helping another general's plan to success, will reduce or cancel prior warnings. And this kind of behavior can be encouraged on successively lower levels - get your generals to encourage cooperation among those under them, and so on, until the entire organization is built that way.
Also, stop rewarding cutthroat behavior! Market it as loyalty, loyalty to your organization, your cause, and to you. Someone brings you info (about their peers, subordinates, superiors) that advances your organization or prevents a loss, they get rewarded. Someone brings you something that tears another down but is not helpful to your goals - they get neutral-to-outright-cool treatment, since minor squabbles or rule-breaking can distract from what your actual goals are. Play cutthroat behavior openly as selfishness and sabotage, noting that such a person puts themselves above your goals and that is neither behavior you want to reward, nor the type of person who should rise in your organization.
Make a special point of rewarding anyone, anyone who sets the goal above their ambitions - those who have asked for help, those who have sacrificed for your cause, those who are loyal to you. Pick out some names or instances of those lower down, so that your generals know what qualities impress you and catch your eye (and make sure no-one goes after your examples, please, the best loyalty is two-way). If you can get your hands on some names of those who "torpedoed" their careers by asking for help, bring them up (or create some) as examples to follow and heap their failures onto the heads of those who didn't help.
Really, you want people loyal to you anyway, so just make sure that letting plans or people fail is seen as deeply disloyal because those failures are not helping. This can also serve as a visible reason for your shakeup and new policies. Make sure your supervisors all the way down are looking for competence and loyalty, not competence and ambition (that's a combo likely to bite you, okay?).