Read the mixed armor rules carefully. At no point in time do they mention anything about majority invulnerable saves. They are only meant to handle mixed armor and mixed armor saves. The new Tau codex has two special rules covering this, so you absolutely can use that invulnerable save as manytimes as you can legally allocate wounds to it.
In your case, one wound will be allocated to the broadside and one to the sheild drone. Sounds like you will lose both models (broadside gets no save, and even if the drone makes its save the controller is dead so....)
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