So this is how I tend to deal with spires, especially on maps like this with large amounts of cloud/ cover, (at least the theory of it). It's a specific tactic I like to use, so it wont help in all circumstances, however it synergies with this map quite well.
First up you'll need kerosene, phoenix claw and chute vent (opposite of hydro) and a goldfish equipped with a heavy carronade. You need to make sure you're approaching the enemy from a position of cover, so that they spot you as late as possible. You also need to make sure you're never going into a 2v1. If the ally of the spire you're focusing on can lay disabling fire on you, your victim will be able to escape, reposition and annihilate you. So pick your targets wisely - isolated ships or a ship already engaged by your ally will make the easiest targets.
So here's the tactic:
1: You need to be approaching from above. Due to all the buildings, you'll likely have gained altitude to avoid most of the obstructions. Ships in the centre will tend to stay at lower altitudes due to the lack of cover and multiple directions you can approach from. Another thing to remember is that you cant just fly to the centre, have a good look around, then expect to be able to choose a target; you need to decide your target en route and keep your momentum from your engine burn into the centre of the map going into this manoeuvre. Make sure to be bringing up the mini-map with M to check the position of the ships. If they're spotted this will be a lot easier.
So you've found your enemy, their alone, and it's time to go in for the attack. As you move towards the spire, you need to be burning kerosene (staying above them and out of their arcs) and, if they've seen you, use your stamina as a speed boost on top of the kero and a mini hydrogen to maintain yourself above their arcs (as can be seen on the diagram
-_-).
2/3: So now you're just above the spire, poised for the next stage. Activate chute vent (only for a moment, it will continue on its own for a few seconds after use) and make sure you're pressing s to descend more quickly. As can be seen on the diagram, the balloon extends at the front of the goldfish further than the hull, allowing you to use it as a kind of hook - as you hit the top of the spire, have your gunner ready on the heavy carronade, so he can shoot out their balloon. Once their balloon is broken the spire will be hopefully be in big trouble (you may well get a hull break as well) and their cap will try to outmanoeuvre you, and get his gun arcs on your ship. Just bear attention to your altitude - don't use any more chute vent - and stick to his balloon, having your gunner repeatedly destroy their balloon. Spires die especially quickly on the floor, so don't try to ram unless you have to (or until you gain some more experience with ramming), it's always better to keep your position over ramming, unless you need to get the kill off quickly and help your ally.
After pulling off the first kill, you'll have to brawl with the second spire. Hopefully you'll still have an ally by this point. Even for experienced players, a 2v1 isn't easy and you should pull off the second kill quickly. If you manage this, expect the first spire to be rushing back in to help its ally. They'll likely approach from the South-West (quickest route), so make sure you're pointing that way. In my experience it's far easier playing on the defensive on this map so you should be alright from then on in. Never overly extend when defending, make sure to keep guarding that capture point!
This technique can help you pull off a very quick first kill, especially if they're already at lowish altitude - which is especially important for KoTH as you need to kill both of them in quick succession, before the one you've just killed is back to help its ally. Remember from the first kill to the second, you probably have only about 40s till they respawn and get to the centre again so be wary of that.
