Wait a minute. from your post sounds like your own ships don't get hit by the cannon effects? I thought everyone gets hit. Is this also true for your allies ships too?
Originally, every ship in the well would be damaged. This meant that in the late game, you'd have to turn off all your cannons just to keep them from obliterating your own fleet once you got to the last couple planets. In a patch (1.05?) they changed that; now, friendly vessels (yours, allies, cease fires) aren't stunned or harmed at all. It's VERY nice, especially when the shell lands right in the middle of a large fleet battle.
Umm...it takes a few minutes to cycle, so I'm not sure how useful this would be. The best use is to have multiple cannons shoot one after the other as your fleet is attacking.
It depends on what you want out of it. Generally speaking yes, a kostura shell is at its most effective when used to directly support a fleet's assaults. But, in my experience that has three major drawbacks:
1> Kosturas, after all the AM upgrades, can fire as often as their recharge allows. If you're holding them in reserve until the fleet is ready to attack the next planet, that's a lot of wasted potential; they should be firing as often as they possibly can, because even if they hit the "wrong" system, the stun effect will still be useful to you (economic disruption, slows down fleets passing through). The damage is also nice; even if it doesn't actually kill any structures, any fleets passing through will come out half-destroyed. I've had more than once where a massive enemy fleet attacked my planet with all of its ships already at 50% hull and no shields, making it very easy to wipe them out with an inferior force.
2> The things rotate and fire so slowly that it's very easy to get a wasted shot if you try to time it to land the shell in the middle of a battle; it could easily arrive after everything in the well is dead. Leading off with them is fine (i.e., waiting until you see the shell in transit before giving the fleet the movement orders), but anything more precise than that gets VERY iffy, especially on large/multi-star maps. Waiting for the shell to begin your battle also means you're not attacking as quickly as you could be, giving your enemy more time to rebuild fleets and place static defenses; I get better results from continuing to charge forward and hitting your foe before he's had a chance to recover from the previous planet's beating.
3> The micromanagement needed just isn't really worth it, outside of a few very specific situations. In my opinion you're better off using that time to manage your fleets more precisely. On a very small map, when you'll only have 1-2 cannons, no big deal. On a large map where I might have a dozen or more, you just don't have the time.
So, I generally only hold two or three cannons in reserve for direct support (and to open phase paths for my fleets), and set the rest to autofire. It's great against the AI, and not bad against humans (as you're now less predictable; they don't know which planet is going to go offline for 15s).