The maximum size of the fs exowaves is proportional to the number of spire cities you have, and has no relation to AIP at all. Actually, a fairly recent change made the exowave-budget-increasing spread across the city hub and the city modules (shipyard, hab, reactor) so I guess in theory you could scrap all of those sub-modules at some point to reduce the max size of the exowaves, but I don't know if that would really help you (nor would I be content as a game designer to leave that as a valid tactic, just feels wrong for several reasons).
Anyway, the addition of HKs to the list of ships that can be picked for exos is also a fairly recent change. I've heard some feedback about the pain they can inflict, but I don't recall anyone saying they presented a total brick-wall to progress (at least not at this stage of the game). So it's possible they're a bit much but I think you can probably eke by during that last 30 minutes or so:
1) Know where the HKs are. And anything else that is truly a threat.
2) Have your spire capital fleet waiting for each HK as it emerges from a wormhole (any wormhole will do, so long as you aren't under particularly withering fire), so that you're right on top of the HK and it doesn't get to use its range advantage, and just blast the thing to smithereens. Nothing in the game can withstand the full firepower of a spire fleet for very long, though you are still going to suffer losses.
3) As an alternative to 2, only face the HK while your fleet is under spire city shields (and not human ffs, as the human ones reduce outgoing firepower). Normally I place my cities covering inward-facing wormholes but in theory you could put one right next to one that you know the AI has to come out of to get to your homeworld, and tear it up good right as it comes out (but they can then still rush past you to the next wormhole, if they survive).
4) Defense in depth.
- The normal speedbumps (an ff over every inward-facing wormhole) won't actually slow down an HK much if at all, but a significant defensive bulwark (a spire city, or a big pile of human ffs) can.
- Also, sheer distance can work in your favor: the exos have to spawn from an AI planet, so before starting the transceiver-attacks phase you can take your spire fleet and do a clear-cut of all AI planets out to some distance. AIP will go through the roof, but that won't be an issue unless you have golems-hard or spirecraft-hard enabled (and even then it probably won't make the difference between win and lose in this particular case).
5) If you do have spirecraft, I commend implosion artillery to you for HKs and anything else with an unsanitarily-high max hp. Rams may also be good, haven't tried those much myself.
Good hunting