There is an alternative to an STC. There's such thing as a "field approval." If you can convince an FAA inspector that you don't need that gear door, and he's willing to sign off the paperwork, then a Field Approval is like a one-time STC for that aircraft only. Good luck with the FAA.
But I do agree, that gear door is retracted at lower speed (i.e., less drag). But provides slipstream during higher speed cruise & descent.
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