Thanks, trimming and joining worked on the dome and is a nice addition to my bag of tricks. :)

I tried the same thing to join the engine platform to the saucer, but it took a long time to calculate and the end product was a joined surface, not a solid.

[Edit]

I seem to have succeeded by first moving the engine platform down ever so slightly, then the boolean union to the saucer worked. Then I trimmed and joined the dome on. Hopefully this works for the final! :)