AI homeworlds are completely invulnerable to nuke, by virtue of homeworld guard post, command stations, and ships mark V being 100% immune to nukes.
Lightnings and Armored warheads does work.
You can wait till your resources are maxed and launch a beachhead + your fleet into the homeworld to grind down the strategical reserve. Avoid fleet wipe and make raid to lower the strategical reserve down to 1%, then there will be far less ships to bother your fleet while you go killing the AI guard posts.
Otherwise it's up to raiding the guards posts with not-too expansive fleet ships (perhaps a couple flag) through transports, possibly using other transports as a distraction, with your fleet maybe swapping in and out of AI homeworld.
The strategical reserve is the huge thing, it's what you can throw warheads at to reduce, and once you kill it, it's much easier to hold a beachead on the AI homeworld and finish it.