Go upwind, and use the surge of transformation to create a caustic gas that chokes and poisons. The point isn't to kill the radiants (it won't) but to kill the mundane soldiers, damage stormlight reserves and hurt morale. When the windrunners and skybreakers try to stop this, ambush them, and kill as many as you can.
Wait for the gas to clear out. Maybe a day or so.
Next up, your goal is to kill the soulcasters. Secret spren should be able to scout out the castle; look for where they sleep, and record it. Prepare some Metcha-Im, and load them up with Boulders. Strike where they sleep under the cover of night; all going well, you'll crush the wall and maybe crush them. Send in a Nex-im to make sure they're dead: cut their heads off with one of the aluminum shards and hold it until the other radiants come and kill you.
While this is happening, on another spot, shoot more Boulders close to the ground and have a full assault; thunderclasts, magnified ones, deepests ones ect.
Throw some Tatak-im into the moat to fill the air with boiling steam, destroying visibility, and removing the issue of the moat.
Let some flowing ones scale the walls while this is happening- they can't stop us all. They're mostly trying to distract the radiants.
Heavenly ones aren't attacking, moreso trying to keep everyone grounded.
The goal isn't to kill everything; the higher radiants will be very hard to put down, so just try to ignore them. Thin out the numbers and damage the fortress itself. Take away all the aluminum you can find.
Once the strike begins to turn, retreat, and recover. Wait for the next highstorm to allow more fused to come back, but in the meantime, harass them with deepest ones and make them kill their friends with the faceless ones.
Of course, this means the radiants have more investiture; but that shouldn't be a problem.
After a few days, strike with the infantry and everything else; the exact options don't matter, since fully repairing the fortress Is impossible. Now you kill everything