Okay, I think I figured it out.

I used the Falcon Peak model, but I stripped it of all its weapons and used 2 Ultimas, 2 Antennae, a Firaga, a Blizzaga and a Meteor. I also used all three Laser upgrades. Problem solved! This also worked for some problem spots on Mission 2.

Now I'm stuck on Mission 3. I've got everything except a Firaga which is supposed to be dropped behind the ship by a red Hex Ring. It comes after a Red Speeder, which comes after the second Reaper's Wheel. I need help again!