In my test game I would often get 2k-3k stalking-blobs next to my spire-city defense planets. Basically the firepower of the cities (and capital ships if you station them there) is so high that the AI ships won't attack until they have a similar amount. And that takes an awful lot of fleet ships
This tends to result in them piling up a really mammoth swarm that comes through with the next sufficiently-large exogalactic strikeforce (which often includes high-firepower ships of its own). This can be quite a strong attack, and a game-ender if you're not particularly well set up for it.
Currently there's one very easy way of dealing with them, though:
1) Move an EMP MkII and your entire Spire capital fleet to your side of the wormhole.
2) Send the EMP through, boom.
3) Send your Spire fleet through and turkey-shoot the emp'd AI ships.
I've managed to destroy 2000 AI ships (on low caps) before an EMP II wore off. In some cases an EMP III may be warranted. If even that won't do it, just pull your fleet back before the emp wears off (unless you think the fleet can now take them, of course).
If you don't want the AIP of warheads, and you have an alternate path into the system with the stalkers, you can send your spire fleet around and into the system from the "back entrance" and this tends to "spook" the AI ships into flying into your planet. This can backfire, as they may overwhelm your less-defended city before your fleet can catch up and do enough damage.
If you're bottlenecked, and don't want to spend AIP, you may be able to provoke an early attack by temporarily pulling your capital ships back and thus changing the firepower value of the defense planet by quite a bit, and the AI ships will rush in. In theory they'll retreat if you rush back in and overwhelm them but in theory I've found that the firepower difference is not enough for them to "take their ball and run". Even if they do, there are various tricks (notably engine damage and paralysis) you can use to whittle them down while they're on-planet.
Later on I want to make the stalking smarter than "gee, let's sit directly on top of their doorstep so they can lob explosives at us", so some of these would be less trivial, but this is how it stands for now.