As a purely hypothetical and academic discussion...

Soldiers going Postal and killing commanders in the US armed forces is a very different level of blowback to supporting Genocide than dealing with protesters in the streets. A certain level of protest and ill-will from the population is factored in to these decisions: losing career commanders is not. If you're going to go out and set an example for how to refuse to take part in an organization that aids a genocide, you may as well do as much damage as you possibly can. There's no moral duty to go easy on genociders, even if they're one degree of separation removed.

As for your argument about whether or not it would be twisted by the media - of course it would. But with a proper letter of intent drafted and mailed to multiple media outlets and unaffiliated journalists, at least some exposure to the true messaging could be achieved. This isn't an atmosphere of unilateral control over the media like was possible in the 80's and 90's, and people are more open to dissenting voices now than ever. There's already high profile examples of officials resigning that could be pointed to as well.

https://www.reuters.com/world/us/us-education-official-resigns-over-bidens-israel-gaza-policy-2024-01-04/#:~:text=Josh%20Paul%2C%20a%20former%20State,%22blind%20support%22%20for%20Israel

It's not some fringe crank position to be anti-israel at this point. The resignation was almost 4 months ago. That there hasn't been any escalation of resistance is more surprising than anything. I genuinely think if you're in the armed forces and have decided you're willing to die for this moral issue, we're at a point where it's both morally and strategically viable to harm the structure as much as possible on the way out.