Xenosaga comes to mind (in both the game and TV show). In the last episode of the show (or the last part of the game) there is a space station (Protomerkaba) that in the end is set to "detachment" (a.k.a. self destruct, in most sci-fi films). And it literally falls apart one piece at a time. Then at the LAST moment the goodguys get cargoship Elsa out of there before it completely destroys them.
Now for the Miyazaki connection. There is a similar floating fortress called Laputa, In the end it is set to self destruct with the "destruction" spell, and it falls apart in a VERY similar manner to Protomerkaba's destruction in Xenosaga. Then at the LAST moment before the falling debris crushes them, the Dola Gang (sort of like anti-heroes here, they are "good" pirates) escapes like the crew of illegally modified scavenger ship Elsa (who are themselves sort of like pirates picking up useful ship debris after battles) escapes in a VERY similar "close call" manner.
Let me also look at Escaflowne. You have Hitomi ending up in a weird place she's unfamiliar with as Sheeta does in Castle In The Sky. You have Hitomi with a long elliptical crystal necklace, but Sheeta also has a similar necklace with elliptical (though her's is more teardrop shaped) crystal. Both have mysterious powers that must be tapped. Both run into a previously unknown male counterpart who they go on adventures with to achieve some ultimate goal. The Zibach floating fortress in Escaflowne is much like the castle Laputa in terms of its levitation and being a big base where one can launch attacks from.
Lastly lets look at Evangelion. Several of the Angels have eyes that can fire very powerful laser beams. So can the "Giant Warrior" / "God Warrior" from Nausicaa of the Valley of the Wind (but its beam fires from its mouth). Also these Warriors are huge, just like the Angels. Also the EVAs themselves are not entirely mechanical. They have mostly biological components. Just like the Robots from Castle In The Sky. When you see inside the first captured Robot at the fort, the part where the arm is broken off, you can see inside. But you don't see wires. Instead you see what looks like tendons and guts! Not to mention its eye doubles as a laser gun (much like the Angels in Evangelion). Also in one of the last battle scenes of End of Evangelion (before it just gets all crazy) you see the the Mass Produced EVA series deploy wings and fly, just like the Robot the all of a sudden deploys wings and flys in Castle In The Sky. And the way the Robots swarm around the army's ship and completely destroy it in Castle In The Sky is similar to the way the EVA's swarm around Asuka's EVA02 (now out of battery power) in End of Evangelion, and completely destroy it.