Gyroscopic stabilisation probably wouldn’t work. It would either be so strong you can’t actually aim it, or so weak as to not make any difference. How does it differentiate between minute adjustments and your hands moving from your breath?
Expending expensive electronics with every shot? In an apocalypse? Good luck. Targeting computers are a thing even today, projectile motion is spectacularly easy, but it’s not exact in the real world by a decent margin. You couldn’t possibly account for all the wind currents, tiny hand movements, etc. You’re far better off trying to stabilise a person’s hands, and that’s far better done with bionics. Or better yet, a set of robotic arms holding the thing for them.
Stabilising your hands is exactly what the targeting system CBM does, it helps to make you more accurate.
I don’t think anyone would replace their heart with something electronic just for a bit of extra accuracy.
Look, making humans more accurate is difficult, maybe even impossible. The best you could do is MAYBE make them aim faster, and that would just require implants in hands/arm/brain.